WASHINGTON — Federal prosecutors have obtained records indicating that John R. Allen, the retired four-star Marine general who commanded all American troops in Afghanistan and now heads a venerable Washington think tank, secretly lobbied for the government of Qatar, lied to investigators about his role and tried to withhold evidence sought by a federal subpoena, according to court documents.

The court records are the latest evidence of a broad investigation by the Justice Department and F.B.I. into the influence that wealthy Arab nations like Qatar, the United Arab Emirates and Saudi Arabia wield in Washington.

The records about General Allen were filed in April in Federal District Court in central California in an application for a warrant to search General Allen’s electronic communications.

Other filings in the case appear to remain sealed, and the public release of the warrant application may have been accidental. The filing lays out evidence that General Allen joined in the secret lobbying plan along with Richard G. Olson, a former United States ambassador to the United Arab Emirates and Pakistan, and Imaad Zuberi, a business executive with ties in the Middle East.

Mr. Zuberi is serving a prison sentence for violating foreign lobbying, campaign finance and tax laws, as well as for obstruction of justice. Mr. Olson has agreed to plead guilty for participating in the Qatari lobbying effort in violation of a prohibition on such activity during the first year after leaving diplomatic service.

A spokesman for General Allen, Beau Phillips, said in a statement: “John Allen voluntarily cooperated with the government’s investigation into this matter. John Allen’s efforts with regard to Qatar in 2017 were to protect the interests of the United States and the military personnel stationed in Qatar. John Allen received no fee for his efforts.”

The court documents were reported earlier on Tuesday by The Associated Press.

Federal law requires that anyone lobbying for a foreign government register with the Justice Department. The department has been cracking down in recent years on violations of the Foreign Agents Registration Act, or FARA. There is no record of General Allen registering to lobby for Qatar.

Federal prosecutors have signaled a particular interest in potential violations involving Persian Gulf nations, which have developed close ties to business and political figures in the United States. Last month, the Justice Department filed a new indictment in an ongoing case against Thomas J. Barrack Jr., a friend and informal adviser to President Donald J. Trump, for working on behalf of the United Arab Emirates to steer American foreign policy during the Trump administration.

The plan described in the documents involving General Allen unfolded around the beginning of the Trump administration five years ago, after he had left the military and before he became president of the Brookings Institution think tank. Qatar was frantically trying to fend off a pressure campaign and economic embargo by its Persian Gulf rivals, Saudi Arabia and the United Arab Emirates. Rumors were circulating of a possible Saudi ground invasion, Mr. Trump appeared to back the Saudis and Emiratis, and both sides of the dispute were spending heavily to win favor in Washington.

Mr. Zuberi, according to the filing, “viewed the diplomatic crisis as a business opportunity” and began conspiring to sell lobbying services to Qatar. He contacted Mr. Olson, who had recently left government. Mr. Olson in turn brought in General Allen, according to the filing.

“If we can do this we will own half of Qatar,” Mr. Zuberi wrote to Mr. Olson in a WhatsApp message cited in the filing about their proposed plan with General Allen.

The court document gives a detailed account of several weeks in June 2017 when General Allen was recruited by Mr. Olson and Mr. Zuberi to meet with top Qatari and American officials to diffuse the Gulf crisis — and how General Allen saw the money making potential for his involvement.

The document states that he agreed to travel to Doha, the Qatari capital, at Mr. Zuberi’s expense and negotiated a payment of $20,000, which he referred to as a “speaker’s fee.” The document quotes one message from General Allen showing his aim of making more money down the road — to “work out a fuller arrangement of a longer term relationship.”

Other messages cited in the document show that General Allen pursued other business with firms affiliated with Qatar, one of which would have provided him with a commission of over $1 million. The document said the F.B.I. has not determined whether he received this money.

During this period, General Allen met several times with American officials, including members of Congress and H.R. McMaster, the retired three-star general who was then the White House national security adviser. But the document, citing an interview of General McMaster by federal agents, stated that General Allen never informed General McMaster that he was being paid for his work.

The document also described efforts by General Allen to obstruct the investigation by lying to federal agents who asked him about his lobbying efforts during an interview last August, and withholding documents that showed his financial interest in his interactions with Qatari officials.

“Allen’s production was devoid of any documents that revealed his financial interest in the diplomatic crisis and nearly devoid of any documents showing the involvement of Zuberi and Olson,” the search warrant states.

General Allen is a former deputy commander of United States Central Command, which has responsibility for the Middle East and a large base in Qatar.

His time at Central Command helped him cement ties with senior Qatari leaders, including Sheikh Tamim bin Hamad al-Thani, the country’s emir. In 2011, he was given a fourth star and took command of all American and NATO troops in Afghanistan until 2013.

In 2016, the year before the court document states his lobbying effort for Qatar began, General Allen was an adviser to Hillary Clinton’s presidential campaign, and he spoke that year at the Democratic National Convention.

He took over as the president of Brookings in November 2017.

Brookings once had a large campus in Doha. The campus was established years before General Allen became president of the think tank. In September, according to its website, Brookings ended its affiliation with the Doha institute, which is now called the Middle East Council on Global Affairs.

Mr. Olson’s contemporaneous notes on a June 2017 conference call show that Mr. Zuberi agreed to pay the group’s travel expenses and General Allen’s speaking fee but emphasized the need for secrecy.

The filing suggests that General Allen sought other forms of payment as well. An Israeli security company, Fifth Dimension, had agreed to pay him $10,000 a month as well as a 1.5 percent commission on any new business he generated, and he sought credit for persuading Qatar to sign a $72 million contract with the company over the same weekend trip — potentially earning him a fee of more than $1 million.

His endorsement “would likely complete their decision making,” he wrote to the company in an email quoted in the filing.

General Allen also sat on the board of a Texas-based artificial intelligence company, SparkCognition, and appears to have attempted to sell a $30 million contract for its services to Qatar as well. “The brief is in their hands,” General Allen wrote to the chief executive shortly after returning from his visit.

General Allen appeared to acknowledge that he was in effect working as a subcontractor on the lobbying effort, most notably after the Qatari emir and other top officials insisted on excluding Mr. Zuberi from a meeting with the former general and the former ambassador.

“You guys should have stepped in and said no you should stay,” Mr. Zuberi fumed in a WhatsApp message to the ambassador, adding, “Does General Allen know his place or his position?”

In an email to make amends, General Allen, according to the court documents, thanked Mr. Zuberi “for his leadership” and expressed regret at his exclusion. “I think there is a lot of opportunity,” he added.

Mark Mazzetti reported from Washington, and David D. Kirkpatrick from New York. Seamus Hughes contributed reporting.