Moscow will keep trying to stir anti-American sentiment in India, including more hints of CIA complicity in the assassination of prime minister Indira Gandhi, to keep India's new leader, Rajiv Gandhi, from moving toward friendlier relations with Washington, western diplomatic sources here say.

The sources said this was a high-stakes gamble by the Kremlin because the effort is deeply resented by the Reagan administration. The Soviets risk "damaging very severely any hope of improving U.S.-Soviet relations" if they keep up that campaign, one diplomatic source said.

Moscow Radio first sought to link the CIA to the Sikh bodyguards who killed Gandhi one day after she was shot on Oct 31. Since then, the Soviet news agency Tass and Communist Party newspaper Pravda have continued to publish suggestions that "external forces," implying the United States, were behind a conspiracy.

President Reagan called the Soviet reports the "world's biggest cheap shot." Secretary of State George P. Shultz said he "forcefully" complained to Soviet Prime Minister Nikolai A. Tikhonov on Nov. 3, when they met here after Indira Gandhi's funeral.

Shultz told reporters afterward that Tikhonov said "he had looked into it and the Soviet Union had no such view."

The Soviet reports have continued, however, appearing in Tass on Nov. 4 and Pravda on Nov. 5, and they have been passed along from Moscow by the Press Trust of India, an Indian news service. Sources here said this suggests that either Tikhonov was lying, or was not speaking authoritatively, or that Shultz misunderstood what Tikhonov was saying in the private meeting.

Whatever the case, one diplomat said, "I can't see them the Soviets backing off. They are uncertain enough about the current situation here, and uncertain about how Rajiv will go, so that they will keep it stirred up."

The Associated Press said all Indian cities were reported quiet Wednesday for the second day running but, as a precautionary measure, the government prolonged until Nov. 18 its ban on assembly of more than five persons. Army troops patrolled the streets of New Delhi and at least 27 other north Indian cities. Night curfews remained in force in 103 towns.

Reuter news service reported that a senior security officer was named to head an investigation of the Gandhi assassination and a major shakeup of internal intelligence was announced.

Referring to Moscow's hints of U.S. involvement in the assassination, another diplomat said, "The Soviets are probably just getting geared up. I don't think we have seen the end of it."

He forecast the Soviets will keep the allegations alive to see how they are received by Indian newspapers, apart from the communist press. Thus far, the Soviet charges do not appear to have had much impact here and they have been condemned by a number of newspapers.

The sources said they believed, however, that the Soviets could continue such a campaign as long as the formal Indian government inquiry into the assassination is under way, which could take several months.

In the past, India has proven to be fertile ground for Soviet disinformation campaigns, the most recent of which was launched last year when communist-oriented newspapers published what was purported to be a secret cable drafted by U.S. Ambassador to the United Nations, Jeane Kirkpatrick, outlining a U.S. strategy to promote the Balkanization of India and thereby subvert Soviet influence in the region.

Photographs of what the U.S. Embassy here said was obviously a forged State Department cable appeared in several Indian papers and became the focus of a brief debate in Parliament until the U.S. government countered with evidence that remarks about India in a speech Kirkpatrick had made before a conservative group in Washington had been lifted out of context, altered and put into the false cable.

"We are expecting other disinformation campaigns. There will be a major preoccupation with attempting to influence him Rajiv Gandhi against the United States," one diplomatic source said.

Both the slain prime minister and her son have often alluded obliquely to "foreign forces" that they said were bent on impeding India's development, but western political analysts have been uncertain whether Rajiv Gandhi made the comments to accommodate his mother or whether he actually believes that a conspiracy of external subversion is behind religious and civil unrest in India.

One diplomat said he thought Rajiv Gandhi, then the most influential of five Congress (I) Party general secretaries, may have made his comments about the vague "foreign hand" to placate hard-liners in the party.

The diplomat noted that when a voluminous government white paper on the Indian Army's assault on Amritsar's Golden Temple complex was issued in July, it made no mention of the United States despite some uncorroborated charges made publicly here that U.S. and Pakistani intelligence agents were involved in assisting and training Sikh separatist guerrillas in Pakistan.

Shortly after the white paper was issued, the Congress (I) Party published a pamphlet entitled "Conspiracy Revealed" in which the United States was mentioned in connection with external subversion. The move was seen as an an attempt to appease party hard-liners upset by the tenor of the white paper.

Western diplomats said Gandhi's succession presents an opportunity for the United States to improve relations with India, which have been strained over increasing U.S. arms supplies to Pakistan.

Characterizing Rajiv Gandhi as more pragmatic and western-oriented than his mother, a western diplomat said he expected the new prime minister to at least "bring around a rethinking of relations with the United States."

"For the moment, we see no reason to doubt he will be more western and more open," he said.

Offsetting that prospect is the probability that the new prime minister will not tamper with Indian policies that are influenced by the country's role in the Nonaligned Movement and its enduring economic and military ties to the Soviet Union.

Complicating the equation is the influence of those policy makers in Washington who favor increasing military aid to Pakistan even at the expense of hurting relations between the United States and India. Similarly, there is the influence of some Indian foreign policy advisers who have consistently resisted closer ties to the United States until it scales down its military commitment to Pakistan, diplomatic observers said.

Additionally, the Reagan administration will have to consider the effects of other irritants to its relations with New Delhi, such as U.S. opposition to Asian Development Bank loans to India.

But a hopeful sign, diplomatic observers said, is that a U.S. delegation will be arriving here next week to discuss increased transfer of technology to India. The Indian side in the talks will be headed by a high-ranking official in Gandhi's government.

Reuter reported the following:

The Press Trust of India said the Home Ministry announced several key changes among senior police officers in charge of the prime minister's security when she was killed.

A ministry statement said S. Anand Ram, director-general of the Central Industrial Security Forces, was named to head a team to investigate the assassination. The CISF is a paramilitary force that protects state-owned factories.