The Soviet government extended full diplomatic status to the Palestine Liberation Organization today in a clear bid to strengthen its influence with radical Arabs following the death of Egyptian president Anwar Sadat.

Diplomats from Moslem countries said the move seemed to be designed to consolidate the so-called Rejectionist Front of Arab states, which adamantly opposes Sadat's policies. It was apparently prompted by fears here that the removal of Sadat and new Middle East settlement proposals advanced by Saudi Arabia may frustrate Soviet efforts to restore its influence in the region.

As a result, the Soviets not only symbolically upgraded the PLO representation here but also rolled out the red carpet for PLO leader Yasser Arafat, according him treatment normally reserved for heads of important allied states.

The timing of the recognition and the warm reception accorded Arafat suggest that the Soviets are trying to counter vigorous American and Western actions since Sadat's death by making the PLO a principal vehicle of their Middle East policy.

President Leonid Brezhnev personally informed Arafat of the decision in the Kremlin this morning, an occasion that received extensive front-page treatment in the Soviet press.

The PLO has had representation here since 1976 but without formal accreditation from the Soviet Foreign Ministry. Arafat himself has visited Moscow almost every year for a decade but has not always been received by Brezhnev. Most recently he was here in July 1980 but neither saw Brezhnev nor received red-carpet treatment.

Arafat tonight told reporters that he was gratified by the Soviet decision, which he described as an important step toward the PLO goal of creating an independent national state.

The extension of full diplomatic status coincided with rumors here that the PLO is contemplating formally constituting itself as a provisional government.

A U.S. official said it was highly unlikely at this stage that the PLO would declare a formal provisional government, since the organization in effect is seen as such by many Third World nations and because such a move would raise problems and create tensions among the group's many factions.

The PLO is recognized at various levels by about 100 nations and international organizations, the U.S. official said, but most countries only grant it partial diplomatic status. Most Arab countries have granted the PLO full recognition, although the Palestinian organization has no office in Egypt, and Jordan does not accredit the PLO representative in Amman.

The majority of the non-Arab nations giving the PLO full recognition are in black Africa and the Far East, the official said.

Yugoslavia, a nonaligned communist nation, is one of few European countries to extend the PLO full diplomatic representation. Austria is one of the few Western-oriented countries to give the PLO special status, allowing it to maintain a cultural office in Vienna.

The PLO has an unofficial office in Washington and has observer status at the United Nations in New York.

Asked for his reaction to the Saudi plan, Arafat cautiously suggested that he could not comment since he was not familiar with all its aspects. Instead, he gave full backing to the Soviet proposal for an international peace conference on the Middle East and sharply denounced American policies.

In Japan Oct. 14, Arafat indicated strong support for the eight-point peace plan Saudi Crown Prince Fahd advanced in August, calling it "a good basis for a comprehensive peace in the Middle East." He declined to elaborate then, except to say the issue would be discussed at the Arab summit in Morocco next month.

Both Arafat and Brezhnev exchanged warm statements of mutual support and trust, according to the official press agency Tass. It quoted Brezhnev as saying that Moscow "consistently advocates support for the just cause of the Arab people of Palestine" in their "courageous struggle for the exercise of their inalienable national rights."

Tass said both men had "laid particular emphasis on the significance of cohesion and stronger unity of action of Arab countries" in the struggle against "the schemes of imperialism and Zionism"

Arafat told reporters that PLO relations with Moscow were "very strong, and we intend to strengthen and develop them more and more." He also hinted that the Soviets might increase aid to the PLO.

Since the Soviets expect that Sadat's death will terminate the Camp David process, they appear determined to use the PLO to forestall Western attempts to move in a new direction and yet retain the principles of the Egyptian-Israeli accords.

By extending diplomatic status to the PLO, the Soviets have moved up one notch the PLO's claim to be the sole representative of the Palestinian people and, as such, a crucial party to any talks on the Middle East settlement.