AUSTIN, Texas — Heavily armed officers delayed confronting a gunman in Uvalde, Texas, for more than an hour despite supervisors at the scene being told that some trapped with him in two elementary school classrooms were in need of medical treatment, a new review of video footage and other investigative material shows. Instead, the documents show, they waited for protective equipment to lower the risk to law enforcement officers.

The school district police chief, who was leading the response to the May 24 shooting, appeared to be agonizing over the length of time it was taking to secure the shields that would help protect officers when they entered and to find a key for the classroom doors, according to law enforcement documents and video gathered as part of the investigation reviewed by The New York Times.

The chief, Pete Arredondo, and others at the scene became aware that not everyone inside the classrooms was already dead, the documents showed, including a report from a school district police officer whose wife, a teacher, had spoken to him by phone from one of the classrooms to say she had been shot.

More than a dozen of the 33 children and three teachers originally in the two classrooms remained alive during the 1 hour and 17 minutes from the time the shooting began inside the classrooms to when four officers made entry, law enforcement investigators have concluded. By that time, 60 officers had assembled on scene.

“People are going to ask why we’re taking so long,” a man who investigators believe to be Chief Arredondo could be heard saying, according to a transcript of officers’ body camera footage. “We’re trying to preserve the rest of the life.”

Investigators have been working to determine whether any of those who died could have been saved if they had received medical attention sooner, according to an official with knowledge of the effort. But there is no question that some of the victims were still alive and in desperate need of medical attention. One teacher died in an ambulance. Three children died at nearby hospitals, according to the documents.

Xavier Lopez, 10, was one of the children who died after being rushed to a hospital. His family said he had been shot in the back and lost a lot of blood as he awaited medical attention. “He could had been saved,” his grandfather Leonard Sandoval said. “The police did not go in for more than an hour. He bled out.”

Supervisors at the scene at some point became aware that there were people inside the classrooms who needed saving.

“We think there are some injuries in there,” the man believed to be Chief Arredondo said several minutes before the breach, according to the transcript. “And so you know what we did, we cleared off the rest of the building so we wouldn’t have any more, besides what’s already in there, obviously.” It was not clear from the transcript whom he was speaking to.

But even with additional documents and video, much about the chaotic scene remained unclear, including precisely when Chief Arredondo and other senior officers became aware of injuries inside the classrooms. It is not known whether Chief Arredondo or other officers inside the school learned of the 911 calls from a child inside the classrooms who said that some had been shot but were still alive.

Among the revelations in the documents: The gunman, Salvador Ramos, had a “hellfire” trigger device meant to allow a semiautomatic AR-15-style rifle to be fired more like an automatic weapon; some of the officers who first arrived at the school had long guns, more firepower than previously known; and Chief Arredondo learned the gunman’s identity while inside the school and attempted in vain to communicate with him by name through the closed classroom doors.

But with two officers who initially approached the door shot at and grazed, Chief Arredondo appeared to have decided that quickly breaching the classrooms without shields and other protection would have led to officers possibly being killed. He focused instead on getting other children out of the school while waiting for additional protection equipment.

The response by the police at Robb Elementary School is now the subject of overlapping investigations by the Texas state police and the U.S. Justice Department. It was the subject of a closed-door hearing at the State Capitol in Austin on Thursday that featured the director of the state police, Steven McCraw.

But details of what took place inside the school have been slow to emerge, and aspects of the early accounts delivered by Gov. Greg Abbott and top state officials, including Mr. McCraw, have had to be amended or completely retracted. The official narrative has shifted from a story of swift response by the local police to one of hesitation and delay that deviated from two decades of training that instructs officers to quickly confront a gunman to save lives, even at a risk to their own.

Now, more than two weeks after the gunman killed 19 children and two teachers, a clearer picture of the timeline of events and the police response has emerged, according to a Times review of law enforcement documents and video gathered as part of the investigation into the shooting.

A cascade of failures took place at the school: the local police radio system, later tests showed, did not function properly inside the building; classroom doors could not be quickly locked in an emergency; and after an initial burst of shooting from the gunman, no police officer went near the door again for more than 40 minutes, instead hanging back at a distance in the hallway.

According to the documents, Chief Arredondo, who had earlier focused on evacuating other classrooms, began to discuss breaching the classrooms where the gunman was holed up about an hour after the gunfire started inside the school at 11:33 a.m. He did so after several shots could be heard inside the classrooms, after a long lull, around 12:21 p.m., video footage showed.

But he wanted to find the keys first.

“We’re ready to breach, but that door is locked,” he said, according to the transcript, around 12:30 p.m.

By that point, officers in and around the school had been growing increasingly impatient, and in some cases had been loudly voicing their concerns. “If there’s kids in there, we need to go in there,” one officer could be heard saying, according to the documents. Another responded, “Whoever is in charge will determine that.”

A team made up of specially trained Border Patrol agents and a sheriff’s deputy finally went in after the gunman and killed him at 12:50 p.m.

The team entered, not over the objections of Chief Arredondo, but apparently not fully aware that he had given the go-ahead after holding officers back for more than an hour, according to a person briefed on the team’s response by a federal agent involved in the tactical effort. Amid the confusion and frustration in the hallway, the agent believed that the team was taking the initiative on its own to go into the classrooms.

The lack of clear orders underscored the chaos and poor communication in a response that included dozens of state and local police officers, sheriff’s deputies and federal agents from the Border Patrol, many of whom lived or worked nearby.

The delayed police response was part of a series of apparent failures in security that initially allowed the gunman to gain access to the school and classrooms inside, according to the documents from the investigation.

Investigators found that not only did an exterior door — through which the gunman entered — fail to lock, but most of the school’s interior doors, including those on classrooms, could not be immediately locked in the event of an emergency.

And most of the officers arrived with radios that did not function well inside the school building, according to the investigators’ review, potentially creating communication difficulties and confusion.

The system, installed two decades ago, had been designed for the expansive terrain in and around Uvalde, a town of 15,000 surrounded by ranches and farms 80 miles west of San Antonio, according to Forrest Anderson, who works on emergency management for Uvalde County.

“The system was designed because of prevailing conditions at the time,” Mr. Anderson said, to allow officers responding to an emergency to communicate with dispatchers who might be 30 to 75 miles away.

In the wake of the shooting, investigators tested the radios carried by the Uvalde Police Department, as well as by Chief Arredondo’s school police force, and found they did not transmit effectively inside the school or even just outside of it. Only the radios carried by Border Patrol agents appeared to function well, the review found.

Chief Arredondo arrived at the scene without any radio at all, and used a cellphone for some communications. It was not clear if he ever received a radio.

Chief Arredondo did not respond to several requests for comment. The chief of police for Uvalde, Daniel Rodriguez, also did not respond. Chief Rodriguez was on vacation when the shooting happened and was not present at the school, the city’s mayor, Don McLaughlin, said in a public meeting this week.

At a news conference on Thursday, the Uvalde Consolidated Independent School District superintendent, Hal Harrell, said the district was in the “process of developing a list of actions we can take to strengthen security in all of our campuses.”

He said that would include the hiring of additional school police officers, and that officers would be posted at schools during the summer session. There was not a school police officer at the school when the gunman arrived.

“I want to honor our families at this time with support, love and the commitment to move forward as a district for our students,” he said.

The investigative documents provide additional details about the gunman and the weaponry he acquired.

Before entering the school, he had amassed an arsenal of weapons that included two AR-15-style rifles, accessories and hundreds of rounds of ammunition, according to the documents. He spent more than $6,000.

Mr. Ramos, 18, who dropped out of high school last year in the fall of his senior year, made the purchases legally, using money he appeared to have earned working at a Wendy’s and occasionally doing air-conditioning work for his grandfather, according to the documents.

Among the purchases was the “hellfire” trigger device. It was discovered inside one of the classrooms, but the gunman did not appear to have succeeded in using it during the attack, according to an analysis by the federal Bureau of Alcohol, Tobacco, Firearms and Explosives.

After the gunman entered the school, surveillance footage showed him walking through nearly empty blue and green hallways decorated with uplifting messages and a few balloons. He did not appear to fire until he got to Room 111 and Room 112.

It was not clear why he stopped there. He had been a student at the school as a child, and his time there may have overlapped with at least one of the teachers, Irma Garcia, who taught in Room 112, according to the documents. On the day of the shooting, his cousin was in a classroom across the hall.

Chief Arredondo was among the first officers to enter the school and approach the classrooms where the gunman was.

Two Uvalde Police Department officers, a lieutenant and a sergeant, were shot and suffered grazing wounds after they tried to peer through a window in one of the classroom doors, the surveillance footage showed. The entire group of officers who had arrived by then sought cover down the hallway.

No one would approach the classroom doors again, the video showed, for more than 40 minutes, though well-armed officers began quickly arriving.

Fifteen children had come to class in Room 111 that Tuesday, according to the documents, along with one teacher, Arnulfo Reyes. Eleven of the children died in the shooting, three were uninjured, and one was wounded. Mr. Reyes was shot but survived.

In Room 112, which is connected internally by a thin blue door, there were 18 students and two teachers, Ms. Garcia and the teacher who had called her husband after being shot, Eva Mireles. Nine children were wounded but survived and one was listed as uninjured, according to the documents.

Ms. Mireles’s husband, Ruben Ruiz, who worked for Chief Arredondo as one of six uniformed members of the Uvalde school district’s Police Department, had rushed to the school, and it is now clear from the documents that he informed the responders on scene that his wife was still alive in one of the classrooms.

“She says she is shot,” Officer Ruiz could be heard telling other officers as he arrived inside the school at 11:48 a.m., according to the body camera transcript.

That message appeared to have reached a sergeant from the Uvalde Police Department, who was near Chief Arredondo inside of the school.

“There’s a teacher shot in there,” an officer could be heard telling the sergeant, according to the transcript, just before 12:30 p.m.

“I know,” the sergeant replied.

By that time, heavily armed tactical officers had arrived, along with protective shields. Chief Arredondo at that point signaled his support for going into the room, but began asking repeatedly for keys that would work on the door.

It was not clear from the transcript if anyone had tried the door to see if it was locked.

Around that time, an officer also informed Chief Arredondo of the gunman’s name.

“Mr. Ramos? Can you hear us, Mr. Ramos? Please respond,” the chief said, according to the transcript. Chief Arredondo tried in English and Spanish. Mr. Ramos gave no answer.

During that time, a large contingent of Border Patrol agents with long guns and shields massed near the door.

According to the transcript of body camera video, Chief Arredondo could be heard speaking into a phone, preparing for a breach and asking for someone to look into the windows of one of the classrooms to see if anything could be seen.

By 12:46 p.m. he gave his approval to enter the room. “If y’all are ready to do it, you do it,” he said, according to the transcript.

Minutes later, the team went in.

Mr. Ramos was in a corner near a closet in Room 111, facing the doorway, body camera footage showed. He exchanged fire with the officers as they entered. A bullet grazed a Border Patrol agent who was near the door. One of the bullets appeared to have struck the gunman in the head, killing him.

Across the room, the bodies of children lay in an unmoving mass, according to the documents. A similar cluster of bodies lay in Room 112.

Officers could be seen in video footage rushing a few children out of the room and carrying out Ms. Mireles, who appeared to be in extreme pain. She reached an ambulance, but died before reaching a hospital.

Inside the school, officers scrambled to carry or drag the limp bodies of children, some with severe gunshot wounds to their heads, to a triage area in the hallway.

For a time, the fourth graders’ bodies lay where they had been taken, contorted on blood-streaked linoleum under a large colorful banner. “Class of 2022,” it read. “Congrats!”

Edgar Sandoval and Serge F. Kovaleski contributed reporting.