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NEW DELHI– The Congress Party faced a new crisis on Tuesday after a southern political party threatened to withdraw from the governing coalition if India did not join an international push to investigate alleged war crimes in Sri Lanka.

The possible pullout would leave the beleaguered United Progressive Alliance still in control of the Indian government, but it marks the latest case of arm-twisting by fractious government allies ahead of national elections scheduled for next year.

The Dravida Munnetra Kazhagam, or D.M.K., the opposition party in the state of Tamil Nadu, withdrew five ministers from the governing coalition in order to pressure the government to adopt a resolution in Parliament declaring that genocide and war crimes have been committed against Tamils by the Sri Lankan army and administration. But the party has yet to make the withdrawal official by sending a letter to the president announcing the party’s resignation.

This week, the United Nations Human Rights Council, which includes India, is expected to vote on a United States-backed resolution that urges Sri Lanka to deliver on promises to investigate allegations of a mass slaughter of Tamil civilians as the country’s civil war ended in 2009 and also cites reports about possible continued atrocities. The D.M.K. has called for the United Nations resolution to explicitly accuse Sri Lanka of genocide.

Political parties in Tamil Nadu have often voiced their concerns about the welfare of the Tamil minority in Sri Lanka, the island nation off the south Indian coast, where Tamil rebels, known as the Liberation Tigers of Tamil Eelam, or L.T.T.E, fought to gain autonomy for the Tamil regions of the country.

The D.M.K. said it wanted an independent international body to investigate what it describes as a genocide committed by the Sri Lankan government during the country’s bloody 26-year civil war, The Hindu newspaper reported, citing a statement in Tamil by the party’s chief, Muthuvel Karunanidhi. Human rights activists say that more than 40,000 Tamils died during the war.

Palaniappan Chidambaram, India’s finance minister and a senior leader of the Congress-ruled governing coalition, said the D.M.K.’s absence would not cause the government to collapse.

“The government is absolutely stable and enjoys a majority in the Lok Sabha,” he said, referring to the lower house of Parliament. Mr. Chidambaram, who is from Tamil Nadu, was also one of three senior Congress leaders who visited the D.M.K. chief on Monday, hoping to resolve the issue.

“This is not a crisis,” he emphasized as he addressed reporters Tuesday morning.

The D.M.K. said it was withdrawing 18 legislators from the coalition in the Lower House of Parliament, but the Congress Party, which leads the United Progressive Alliance, looks unlikely to be toppled. That’s because in order for the government to fall, a “no-confidence” vote would need to pass the lower house with a simple majority. Of the lower house’s 540 seats, the Congress Party controls the lion’s share with 203 seats and has enough additional support from outside parties, including 43 seats from two political parties in the state of Uttar Pradesh alone, to defeat any such vote.

Mr. Chidambaram said that the president of the Congress Party, Sonia Gandhi, and Prime Minister Manmohan Singh have been briefed about the D.M.K.’s demands and that all political parties are already being consulted on a possible Parliament resolution on the issue.

“We’re examining the text of the final draft that came up before us last night,” Mr. Chidambaram said, but he added that he was not aware of what stand each political party would take on the issue.

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“We are fully committed to the cause of the Lankan Tamils and an impartial inquiry should happen into the allegations of atrocities against them,” Mrs. Gandhi said Tuesday, according to the Press Trust of India. Mrs. Gandhi’s husband, former Prime Minister Rajiv Gandhi, was killed in 1991 by a female suicide bomber believed to be associated with the L.T.T.E. in Sri Lanka.

Mr. Karunanidhi said the D.M.K. would reconsider the pullout if its demands are met, a position Mr. Chidambaram said Congress members have noted.

The D.M.K. is the second major political ally to threaten to yank its support from the governing coalition. In September, the All India Trinamool Congress, which governs the state of West Bengal, pulled out of the alliance, protesting a package of fuel price increases and pro-business economic changes.

Analysts say that the current standoff maybe just politics as usual as the D.M.K. struggles to draw attention to the plight of Tamils in Sri Lanka, a deeply emotional issue in the Indian state of Tamil Nadu. Over the past week, thousands of students across Tamil Nadu, including in Coimbatore, Tirunelveli and Salem, have fasted , picketed and boycotted classes as they demand an independent investigation into the Sri Lankan government’s treatment of Tamils.

Indian police has issued arrest warrants for hundreds of university students in Chennai who were demonstrating against the Sri Lankan treatment of Tamils.

The recent upheaval in Tamil Nadu has been sparked by the recent release of disturbing photographs of the body of the former Tamil rebel leader’s 12-year old son, who appeared to have been shot at close range in the chest, and a report on the continued abuse of Tamils in Sri Lanka. Many of the 72 million citizens of Tamil Nadu relate to and support Sri Lankan Tamils, with whom they share a common language.

On Tuesday, Parliament was disrupted over the issue, which has drawn heated debate on the House floor in recent days.