The death of Indian Prime Minister Indira Gandhi leaves the world's largest democracy facing a period of prolonged uncertainty, with the potential for greater domestic instability and new tensions with its neighbors, particularly Pakistan, according to analysts here.

But while uncertainty offers opportunities for superpower interference, specialists said yesterday that they expect India's relations with the United States and the Soviet Union to remain largely unchanged in the foreseeable future.

In the view of some analysts and U.S. government officials, Gandhi's assassination may move India over the long term away from close relations with the Soviet Union and toward improved ties with the United States, as her absence makes possible the rise to power of a less confrontational and more pragmatic generation of politicians.

The new prime minister, Rajiv Gandhi, is expected to be preoccupied in coming months with the country's difficult internal situation and elections due in January. He is likely to have little time for foreign policy, an area in which his views are virtually unknown.

India's future foreign policy is of more than just regional significance to the superpowers. This is in part because India is widely believed to be capable of building a nuclear weapon, while Pakistan, its rival during the past four decades since partition, is reported to be approaching that stage. At the same time, superpower rivalry in the region has been intensified by the 1979 Soviet invasion of Afghanistan, the ongoing Iranian-Iraqi war, and U.S. and Soviet naval maneuvers in the Indian Ocean.

In many respects, Gandhi's assassination could not have occurred at a more difficult time, following a summer of heightened tensions between India and Pakistan. Last June, Indian officials charged that Sikh separatist groups active in India were being trained in Pakistan. Pakistan vigorously denied any involvement.

Yesterday, Pakistan was quick to condemn the assassination. President Mohammed Zia ul-Haq said that the people of both nations "continue to carry high hopes and expectations of peace and stability of the region." Within minutes of the official announcement of Gandhi's death, Pakistani Foreign Minister Yaqub Khan said his government had declared three days of national mourning.

In Washington, government and academic analysts speculated about changes in U.S.-Indian relations under India's new leadership. "We don't know an awful lot about Rajiv, I suspect," said one State Department official.

But this specialist and others pointed to several factors that are likely both to block any major improvement in ties between the two countries and to prevent any significant shift in the global balance of power. For more than two decades -- and certainly during the period of Indira Gandhi's rule -- India and the United States have differed in their assessment of what U.S. policy-makers consider to be a potential Soviet threat to the Indian Subcontinent. That difference is likely to persist, a State Department official said. Strong and growing U.S. relations with both China and Pakistan, with whom India has historic tensions, impose limits on how far the United States can go in improving relations with New Delhi, despite an apparent desire to do so. Any significant sales of U.S. military equipment to India, for example, could begin to jeopardize U.S. relations with China. India is heavily dependent on Soviet military supplies, particularly for its modern armor and aircraft. The Indians have tried to diversify their sources of supply, but the relationship with Moscow has been long in the making, under both Indira Gandhi and the 1977-1979 administration of ostensibly prowestern prime minister Morarji Desai, and cannot be reversed easily.

Despite these constant factors, Gandhi's assassination has triggered varying degrees of anxiety in Washington, Moscow and Islamabad, the Pakistani capital.

Washington's concern, a State Department official said, is due in part to the fact that the final week of the presidential election campaign could inhibit President Reagan from making major initiatives, if they appear necessary, or from reacting forcefully to events abroad.

Adding to Washington's uncertainty about how to react, should events in India take a further turn for the worse, is the prevailing view here of India's new leader, Rajiv Gandhi. He is seen as a reluctant politician, almost a Hamlet-like figure, lacking the forceful but shrewd touch that characterized his mother's approach to Indian politics.

In Moscow yesterday, diplomats said that the Soviets were believed to have been reassured by the selection of Rajiv Gandhi to replace his mother, viewing it as a signal of continuity in Indian policies, Washington Post correspondent Dusko Doder reported.

But the diplomats said that Moscow will be monitoring internal events in India with some trepidation in the next several months as the new prime minister seeks to consolidate his authority.

In addition to being India's main arms supplier, the Soviet Union has been New Delhi's most constant great power supporter and a principal trading partner. Since the two nations signed a 20-year friendship treaty in 1971, India has been a major factor in Soviet policies in Asia and beyond, serving, in the Soviet view, as a counterweight to China and as one of the few noncommunist Third World nations with which Moscow has overlapping strategic interests.

In the view of some diplomats in Moscow, Washington's role as Pakistan's principal arms supplier has helped push India into a closer relationship with Moscow.

India has been able to count on the Soviet Union to support its position on controversial international questions, such as conflicting Pakistani and Indian claims on the northern region of Kashmir. India in turn has declined to condemn a number of widely denounced Soviet actions, including the Soviet invasions of Hungary, Czechoslovakia and Afghanistan.

State Department officials express the view that Rajiv Gandhi will be so busy coping with internal problems that he will be in no position to undertake foreign policy initiatives -- or adventures -- any time soon.

But some scholars believe that the new prime minister might eventually move to improve relations with Pakistan. He must do so, however, in a way that does not make him appear to be weak, said Thomas Thornton, a former government official who is now a professor of Asian studies at the Johns Hopkins School of Advanced International Studies.

Stephen P. Cohen, professor of political science at the University of Illinois, says there was no evidence that Pakistan meddled in any significant way with the Sikh separatist movement. Neither Pakistan nor India has a reason to initiate military action, Cohen added. In a major war, India would win, but the cost would be "enormous," he said.