India has strongly protested to the American ambassador here the issuance of a visa to the leader of a secessionist movement, calling the action a needless irritant in already strained relations between the two countries.

Foreign Minister P.V. Narasimha Rao summoned Ambassador Harry Barnes to the Foreign Ministry yesterday to express India's "serious concern and unhappiness" with Washington's decision to allow the self-styled president of "Khalistan," Jagjit Singh Chauhan, to visit the United States.

Government officials have termed the American action granting him a visa "an unfriendly act" and a "gross violation" of a U.N. declaration against interfering in the internal affairs of other states, especially since Chauhan's Indian passport has been declared invalid.

In Washington, a State Department spokesman said a waiver of the passport requirement had been granted and noted "humanitarian considerations" had figured in the U.S. decision. In a statement, the spokesman added: "We see no reason why Indo-U.S. relations should be adversely affected by this action. Our decision certainly does not indicate any sympathy for Dr. Chauhan's movement. The U.S. has strongly and consistently supported the unity of India . . . . Our decision to admit Dr. Chauhan in no way detracts fromthis . . . ."

India has never charged Chauhan with any crime, even though he openly advocates the seizure of a large area of the Punjab, India's breadbasket, to create a separate nation called "Khalistan" for Sikhs, a reformist offshoot of Hinduism.

India has a long history of supporting national liberation movements, which Chauhan claims are similar to his Khalistan movement. His movement appears to have limited support among Sikhs in this country.

Prime Minister Indira Gandhi has said that the movement's greatest strength lies among Sikhs living in the United States and Canada. Some Indian officials have charged that it is a creation of travel agents who use it as a vehicle to try to get Sikh clients permission to move to Western nations as political refugees.

The movement is taken seriously by the Gandhi government since it involves one of the richest sections of the country. The government also fears that any success the Sikhs achieve might encourage other secessionist movements, especially in India's isolated northeast, which have far greater public support.

For that reason, the U.S. action has become a major issue in the Indian press during the past few days. Rao was reported to have called Barnes' attention to the strong editorial protests it sparked and to have warned the U.S. ambassador that the public outcry could spread.

Allowing Chauhan into the United States is seen by many here as showing Washington's implied support for the movement to create a separate Sikh nation. Rao, for instance, was reported to have dismissed as "gratuitous" Barnes' explanation that Chauhan was allowed into the United States without a valid Indian passport as a "humanitarian" gesture so he could continue treatment for a heart ailment in Houston.

Chauhan, who lives in Canada, presently is in the United States, where he has been making statements to a weekly publication in New York, India Abroad, that have helped to fan emotions here.

"The Indian government has used its diplomatic powers to knock me out, but what influence I have got has been demonstrated" by his ability to get the American visa, the Indian Express newspaper quoted Chauhan as having told India Abroad.

Moreover, although he supposedly was visiting the United States for health reasons, he was reported to have told India Abroad that he intends to use his stay to petition the United Nations to grant Khalistan observer status and to complain about violations of Sikh human rights in India's Punjab.

Pointing to his activities in the United States, Rao is reported to have told Barnes that the decision to allow Chauhan into the country would have been better understood here if it had been coupled with a bar on any political activity by him.

While in many ways this issue is minor in the overall context of Indo-U.S. relations, it comes at an unfortunate time. Washington and New Delhi appear to be trying to repair serious strains that have developed as a result of the two nations' opposite views of the Soviet invasion of Afghanistan and the subsequent U.S. decision to sell arms to Pakistan to make it a front-line state against further Soviet expansion toward the Persian Gulf.

Gandhi said in an interview released Sunday that the United States has rebuffed India by offering sophisticated F16 warplanes to Pakistan. "I don't think our relations are as chilly as the weather in the United States," she told U.S. News and World Report. "But there's no doubt that they could be very much better."

India is further upset by the Reagan administration's lack of support for multilateral lending agencies such as the World Bank, by U.S. questioning of a $6 billion International Monetary Fund loan to India, and Washington's reluctance to continue supplying enriched uranium to fuel a U.S.-built atomic reactor at Tarapur because India has refused to sign the Nuclear Nonproliferation Treaty.

New Delhi has accused the United States of breaking a contract by refusing to send more fuel here, and both nations are trying to arrive at an amicable end to the contract.