Soviet President Leonid Brezhnev today urged Palestine Liberation Organization Chairman Yasser Arafat to reject President Reagan's Middle East peace initiative, asserting that the United States shared responsibility for "the tragedy in Lebanon" and that it remains opposed to the creation of a Palestinian state.

In a message to Arafat made public by the government press agency Tass, Brezhnev expressed the belief that the Palestinian cause "will eventually triumph."

Asserting that the United States shared responsibility with Israel for the Lebanese crisis, Brezhnev said:

"It was the United States that supplied the aggressors with their deadly weapons and that provided political and diplomatic cover for the aggression. Today, too, the United States is trying to deny the Palestinians their sacred right to self-determination and to establishing their own state.

"In this hour of trial, I confirm anew that the Soviet Union was and remains on the side of the Arab people of Palestine and their only legitimate representative -- the PLO."

Diplomatic observers here said the message appeared to reflect Soviet concerns following the recent Arab League summit meeting at Fez, Morocco. While there has been no authoritative reaction to the meeting, the Soviet media have implicitly endorsed the Arab peace plan drafted at the summit and emphasized its call for the establishment of a Palestinian state.

The Soviets already had denounced Reagan's plan, which calls for Palestinian autonomy in some form of association with Jordan.

Diplomats said that the absence of polemics between the Arabs and Washington after the Fez summit might have fueled suspicions here that a new political situation was emerging in the Middle East from which Moscow might be shut out . It is pointed out that even Arafat has been relatively circumspect in his reaction to Reagan's proposals.

In this context, diplomats saw Brezhnev's message as coupling Moscow's reminder of continued willingness to support the PLO politically with warnings that the Palestinians were unlikely to get such backing elsewhere. The Soviet leader also stressed two other themes that have emerged recently in the Soviet media.

The first is that the Palestinians have fought heroically in Lebanon and this, along with their sense of political responsibility, has enhanced the PLO's international reputation. Secondly, they will achieve success if they "further close their ranks in the struggle for their freedom and national independence."

Moscow has long been the PLO's major weapons supplier and has regarded the organization as a major ally in the Arab world. The PLO's defeat in Lebanon and subsequent dispersal to Arab countries raised the possibility of various PLO factions' being dominated by host governments.

By stressing that the PLO resistance in West Beirut was one of the "brightest pages" in the organization's history, the Soviet leader appeared to be encouraging the continued sense of common purpose among the groups making up the PLO.

According to some analysts, the Soviets are trying to discourage the Palestinians from going along with American attempts to find a settlement, presumably anticipating that the Arab consensus may soon evaporate.