India's new prime minister, Rajiv Gandhi, "is certainly inclined to improve relations with the United States," according to an Indian source with access to the inner circles of the new government.

The improvements, if they come, will not be made at the expense of weakening India's important relations with the Soviet Union, the source said, and they will depend in part on how skillfully Washington manages its relations with neighboring Pakistan.

Meanwhile, as communal violence continued to subside, an Indian police spokesman involved in the investigation into the assassination of prime minister Indira Gandhi said Monday that authorities have contacted Interpol to help locate a third man believed to have had a key role in the murder and who is now thought to be in Canada. Related stories, Page A23.

Relations between India and Pakistan, which have fought three wars since the partition of the Subcontinent in 1947, have been strained by a succession of problems since the most recent conflict, in 1971. New Delhi has criticized the Reagan administration's increases in economic and military aid to Pakistan.

"But his mental condition is pro-American," the source, an Indian journalist known to represent closely the views of the leadership, said of the new Indian leader. The source added that Secretary of State George P. Shultz "made a good beginning when he was here" on Saturday and met with Rajiv Gandhi after the funeral of his mother, Indira Gandhi.

A confidential U.S. National Security Council directive issued several weeks ago reportedly had authorized new American efforts to improve relations with India. The directive followed an interagency study pointing up increased U.S. concerns about tensions within India and between India and Pakistan. A U.S. delegation had been expected to travel to India, perhaps this month, for talks on stalemated sales of American high technology equipment to New Delhi.

How any improvement in relations would come about, the source said, is impossible to forecast. India's foreign policy and its government bureaucracy have, the source said, essentially been put into "hibernation" while the new prime minister seeks to establish stability following the assassination and prepares for parliamentary elections due to be held by mid-January

But the picture he paints of Gandhi is of a rather western-style leader, much less imperial in style and less traditionally Indian than his mother, and one whose friends and closest associates tend to be relatively young, urbane, business-oriented "technocrats" like himself.

His Italian wife, Sonia, is also said to be part of the general western influence on Gandhi, who came to politics as a reluctant novice after the death four years ago of his younger but politically more experienced brother, Sanjay. Rajiv, 40, gave up his job as a pilot for Indian Airlines at his mother's instigation to run for and win a seat in parliament and to take a post as one of the secretaries of the ruling Congress (I) Party. Rajiv Gandhi reportedly is fond of modern management techniques and computers.

The two figures said by several sources to be closest to Gandhi are both members of Parliament from the ruling party who are also in their early forties and are longtime associates of the new prime minister.

One is Arun Nehru, a former executive with an Indian paint company who is a relative of former prime minister Jawaharlal Nehru, Rajiv Gandhi's grandfather.

The other is Arun Singh, a former schoolmate of Gandhi who was a senior executive of another Indian firm.

Both men are on the political rather than policy side of government and are said to be active in screening candidates for the forthcoming parliamentary elections. Both are also viewed as likely to help Gandhi revitalize and give a more modern look to his own party. But whether their role will grow beyond party affairs cannot be predicted, the sources said.

Another half dozen mostly young, modern executives also make up Rajiv's circle of friends and associates who have come to be known as the "computer brigade" and whose influence may carry over into the new Gandhi government.

These include Vijay Dhar, a businessman from Srinagar; P.S. Deodhar, chairman of the Electronics Trade and Technology Development Corp.; and M.L. Fotedar, a former aide to Indira Gandhi and a political aide to her son.

A number of Italian business executives based in India are also among the associates of the new prime minister and his wife.