In an apparent bid to improve relations with the United States, India has proposed a friendly end to the contention-filled contract under which the United States supplies nuclear fuel for India's atomic reactor at Tarapur, according to diplomatic sources in New Delhi and Washington.

The Indian government has told the U.S. Embassy here that New Delhi recognizes that the issue is damaging relations between the two countries and has suggested that India is amenable to a friendly parting of the ways on the contract, according to an Indian diplomat familiar with the discussions. But the Indian source and an American diplomat who confirmed this account declined to provide any other details of the Indian overture.

While the diplomats were sounding an optimistic note on ridding Indo-U.S. relations of their single greatest irritant, a senior Indian nuclear official today delivered an implied threat to the United States during a briefing for foreign correspondents at the Bhabha Atomic Research Center here, saying India no longer needs U.S. permission to reprocess the spent fuel from Tarapur.

"There is no question of permission from the U.S. for the reprocessing of the Tarapur fuel. The fuel belongs to us," asserted Dr. Vvinay N. Meckoni, director of the Tarapur nuclear safety group.

[A State Department official said yesterday that Discussions" had been held with India on the subject of the nuclear fuel contract for Tarapur, but he refused to elaborate on the nature of the talks.]

"It looks like the Indians want out," said a U.S. diplomat. "They realize the U.S. is unlikely to keep giving them enriched uranium and the best way to preserve relations between the two countries is to disengage."

But, he continued, the real concern of the United States is to prevent nuclear testing or further explosions by India, and Washington would like to keep the Tarapur reactor under international safeguards to prevent any of its enriched fuel being used for nuclear weapons.

He acknowledged that India will likely begin reprocessing the spent fuel from Tarapur, which would produce plutonium that can be used to make nuclear weapons as well as to fuel peaceful reactors, and said there is nothing that the United States can do about it. [In Washington, a State Department official said that in the event of a lapse in the agreement the United States would urge that safeguards be maintained on the spent fuel from the reactor. The official noted that the safeguards agreement on Tarapur is tripartite in nature, involving the United States, India and the International Atomic Energy Agency and that it was unclear what position India would take on the safeguards agreement covering the reactor itself should the United States no longer be supplying enriched uranium.]

The agreement under which the United States has sent nuclear fuel for the Tarapur reactor was first signed in 1964 and went smoothly until 1974 when India detonated what it called a "peaceful nuclear device," which was widely viewed as the first possible step toward the making of nuclear weapons.

The Indian explosion led to passage of a law that puts bars in the way of the United States supplying nuclear fuel to countries refusing to sign the nuclear nonproliferation treaty, which India contends discriminates against the so-called nuclear have-not nations. Since then, every sale of the enriched uranium to India has been accompanied by sharp exchanges and considerable wrangling, a process that has driven a wedge between the two countries.

Two shipments totaling 38 tons narrowly escaped being vetoed by the Senate last September after an intense lobbying effort by President Carter. India's request for a third shipment is pending, and it is unclear how the Reagan administration feels on the issue, although the Republican platform specifically opposes further sale of nuclear fuel to India.

While there clearly is a move afoot at the diplomatic level to change the supply agreement, India's atomic scientists took the view today that they wanted the U.S. shipments to continue and expressed hope that the United States would live up to the contract.

"I hope that the U.S. government sticks to the letter and the spirit of the agreement," said Dr. H. N. Sethna, chairman of India's Atomic Energy Commission and the scientist responsible for giving India the capability to separate plutonium from uranium and thus set off its 1974 explosion.

But Sethna has been quoted repeatedly in the Indian press as saying this country can get along without the American fuel, hinting that a mixture of plutonium oxide, which would be reprocessed from Tarapur's spent fuel, and uranium oxide for the enriched uranium was being produced here. Today he refused to say whether India's mixed oxide plant was ready to supply fuel for Tarapur.

Meckoni said India will begin using the reprocessing plant at Tarapur, which has been ready to go into operation for four years, by June to reprocess spent fuel from its nuclear reactors in Rajasthan, the desert area in the northwestern part of the country. It will take two to four months to reprocess that fuel, and he said the plutonium is needed for India's fast breeder reactor program.

Calling mixed oxide fuel using plutonium from Tarapur's spent fuel "the best alternative at the moment" for the U.S.- supplied enriched uranium, Meckoni held out the threat that the nuclear wastes from Tarapur would be next into the reactor.

To quiet fears that India was heading for another nuclear explosion, Raja Ramana, the director of the research complex here and one of the architects of the 1974 blast, emphasized today that he saw no need for another explosion for the next 20 to 40 years.