Secretary of State George P. Shultz sought to remove a growing irritant in U.S.-Indian relations today by guaranteeing that India will be supplied spare parts for its U.S.-built Tarapur nuclear reactor near Bombay.

The assurance, certain to anger Democratic congressional advocates of a tough U.S. stand against nuclear proliferation, was given by Shultz following a meeting with Foreign Minister P.V. Narasimha Rao. Shultz also met with Prime Minister Indira Gandhi on the first day of a three-day visit designed to restore some of the warmth in relations between the two countries that has dissipated since Gandhi's state visit to Washington last July.

A spokesman for the Indian government said, "We are satisfied. The problem has been satisfactorily resolved." He said India hopes to get the spare parts "very soon" after details of commercial arrangements have been completed.

Shultz did not specifically mention a presidential waiver of the provision of the 1978 U.S. Nuclear Nonproliferation Act that bans the export of spare parts to Tarapur because of India's refusal to accept safeguards required under the act.

Instead, he said the United States is "prepared to take the necessary actions to supply those parts which are not available from elsewhere."

However, State Department spokesman John Hughes said in a press conference that the Indians had been assured that the Reagan administration is "prepared to take the kind of action that will permit those spare parts to be made available in the United States."

After the press conference, a senior U.S. official said, "A presidential waiver was not mentioned here tonight, but I wouldn't steer you away from that." He said that after months of acrimonious debate in Washington and New Delhi over the spare parts issue, the administration decided that "it's a good time to do it. You just come to the point where you make up your mind and make an announcement."

Hughes said there was no deadline for making the spare parts available, either through a third country or directly by the United States, but both he and Shultz said Washington is concerned about the reactor's safety because of worn-out parts that have forced the shutdown of one of the plant's units amid rising concern about danger of radiation seepage.

Mani Shanker Aiyar, spokesman for the Ministry of External Relations, said the bulk of the parts would come from European suppliers.

In Washington, Shultz's announcement appeared to have surprised officials at the State Department and the Nuclear Regulatory Commission who had been working on the problem. As late as this morning, they said, they had thought Shultz was planning to give Rao vague assurances that the United States would try to work something out if the parts could not be provided through a third country.

But a problem with this approach, a source said, is that at least one key part sought by the Indians--a control-rod drive mechanism --apparently could not be obtained from either West Germany or Italy, the potential alternative suppliers.

Officials made it clear the administration had not fully worked out how it plans to follow through on Shultz's guarantee. "Just how we're going to go about it is still pretty murky," one source said.

After the announcement, a group of 50 House and Senate members sent a letter to the White House declaring their opposition to the sale and pledging an attempt to block it when it is presented to Congress.

Before Shultz arrived, U.S. officials had said that the administration would prefer a third-country arrangement, but that a presidential waiver was still under consideration.

U.S. officials were known to have wanted to avoid invoking a waiver because it would be certain to result in a battle in Congress to override the action and could lead to an entanglement of legal appeals.

The third-country arrangement is similar to the only substantive agreement that emerged from Gandhi's visit to Washington last July, when France was designated as a surrogate supplier of fuel to Tarapur. Use of that loophole to the export ban significantly improved U.S.-Indian relations until the parts issue arose this year.

The visit by Shultz, the highest-ranking U.S. official to travel to India since a short trip by then-president Jimmy Carter in January 1978, appeared to ease strains between the two countries. Besides the Tarapur issue, these have centered on U.S. attitudes toward multilateral bank assistance to India, including Reagan administration opposition to Indian borrowing from the Asian Development Bank, and what is perceived here as U.S. foot-dragging on grants and soft loans by the World Bank's International Development Agency.

Fresh from her stewardship of the seventh Nonaligned Summit conference here last March, which was dominated by demands for a new international economic order and world monetary reforms, Gandhi was said to be prepared to appeal to Shultz's background as Treasury secretary and budget director and press the multilateral bank assistance issue to the fullest.

Details of Shultz's private meeting with Gandhi today were not disclosed, but Aiyar said senior Indian officials discussed with Shultz the proposed $2 billion Asian Development Bank loans, in increments of $500 million spread over four years.

The Reagan administration has sought to discourage India from borrowing from the Asian bank because it already is a major borrower from the World Bank and other international lending agencies, and because China may become a major drain on the Asian bank's resources.

Indian officials said that discussions were held with Shultz about the Nonaligned Movement's appeal, spearheaded by India, for an international conference to reform the world monetary system. Disappointed by the lukewarm reaction to the proposal by developed nations at the Williamsburg economic summit and the sixth session of the U.N. Conference on Trade and Development in Belgrade, India has stepped up its appeal for a global summit starting with Shultz, officials said.

Aiyar said Indian officials obtained an "assessment" by Shultz for the economic conference proposal, but he would not elaborate.

"If the purpose of this exercise had been to clinch the proposal we would have pushed it further," Aiyar said, adding that India's purpose was to explain its position and get Shultz's reaction.