NEW DELHI — Two young demonstrators were killed on Friday in India’s eastern Jharkhand State amid protests across South Asia by Muslims angered by a comment from an official in India’s governing party that they believe profaned the Prophet Muhammad.

The protesters were shot during demonstrations that erupted after Friday Prayers in Ranchi, Jharkhand’s capital. Protesters there called for the arrest of Nupur Sharma, a spokeswoman for Prime Minister Narendra Modi’s party, who last week made speculative comments on a television talk show about the relationship between the prophet and his youngest wife.

That comment, along with another about the prophet, made by Naveen Kumar Jindal, also an official in the governing Bharatiya Janata Party, prompted outrage across the Muslim world, forcing the government to try to contain the growing diplomatic fallout.

Since taking office in 2014, Mr. Modi has often been accused of stirring anti-Muslim sentiment or remaining silent when Hindu nationalists attacked Muslims, but his government appeared to take swift action after 17 Muslim nations condemned the remarks and lodged official diplomatic protests.

Iran and Saudi Arabia, which often cannot agree on anything, both summoned India’s envoys in their capitals to complain.

In response, the Bharatiya Janata Party, often referred to as B.J.P., suspended Ms. Sharma and expelled Mr. Jindal. The party issued a statement about how it respects all religious traditions and denounces insulting religious figures.

Protests have sprung up in the past week across India, Pakistan and Bangladesh. In Ranchi on Friday, demonstrations began peacefully but turned violent, said Sayub Ansari, one of the demonstrators.

“It was a peaceful protest — nothing was happening except sloganeering to arrest Nupur Sharma,” Mr. Ansari said of the thousands who took to the streets after leaving mosques. “Then the crowd was slowly turning out of control.”

The police charged the crowd with batons, Mr. Ansari said, and protesters pelted stones in return. Then the sound of gunfire sent people fleeing, he said.

Two protesters were shot to death, including Mudassir Alam, 15, who was shot in the head, according to his uncle, Mohammad Shahid Ayyubi. According to Indian news reports, dozens of other demonstrators were injured, as were some police officers; they were treated at a nearby hospital.

“It seems the police here are not trained to control crowds that he got shot in the head,” Mr. Ayyubi said.

The other protester killed in Ranchi, Sahil Ansari, whose age was not immediately confirmed, was said to be on his way home when he was hit by a bullet, according to various news reports.

About 330 miles away, in Prayagraj, a city in Uttar Pradesh, a state governed by one of B.J.P.’s most vociferous Hindu nationalists, the police fired tear gas and charged protesters with batons after motorcycles and carts were set on fire and rocks were thrown. At least 10 police officers were injured, said Prem Prakash, the additional director general of police in Prayagraj.

In Islamabad, the capital of Pakistan, on Friday, thousands of protesters briefly scuffled with the police as they tried to reach the Indian Embassy.

A notable exception to the nations condemning the B.J.P. officials’ comments has been Bangladesh, whose leader, Sheikh Hasina, enjoys close political ties with Mr. Modi.

Nevertheless, tens of thousands of people took to the streets in its capital, Dhaka, and other parts of Bangladesh demanding that the Hasina government join in the condemnations.

“This regime believes that they are dependent on India to retain the power,” said Asif Nazrul, a law professor at the University of Dhaka and a political commentator. “So they are not willing to do anything that makes India angry or displeased.”

Also on Friday, the family of a Muslim student leader, who has led protests against a ban on students wearing hijabs in Indian schools, were detained in Prayagraj.

The parents and younger sister of the student leader, Afreen Fatima, were taken from their home by the police. Ms. Fatima, 24, said she was not involved in Friday’s protest, but she has led lead demonstrations in Prayagraj against the hijab ban in the southern Indian state of Karnataka, as well as marches, in 2019, against a law that offers fast-track citizenship for non-Muslim refugees.

Prayagraj police told the local news media they had evidence against Ms. Fatima’s father — an activist and community organizer whom she said was also not involved in the Friday protest — and were collecting evidence against her related to their political activities.

Saif Hasnat contributed reporting from Dhaka, Bangladesh.