The United States pressed Israel yesterday to ease military pressure against Beirut in order to allow breathing room for continuing negotiations that seek an end to the armed Palestinian presence in the Lebanese capital.

Informed sources said the U.S. efforts, which began Sunday, were given new impetus early yesterday by a strong protest message from King Fahd of Saudi Arabia. The Saudi monarch, in turn, is reported to have acted after hearing from anguished Lebanese Prime Minister Shafiq Wazzan.

Fahd's message indicated that the oil kingdom's behind-the-scenes role in arranging a political settlement in Lebanon was being jeopardized by the intensified Israeli threat against Beirut, according to the sources.

By the end of the day, which saw stepped-up Israeli military action in and around Beirut, administration sources reported clear signals that the pressure would be eased.

Deputy presidential press secretary Larry Speakes, speaking on behalf of President Reagan, called for observance of the cease-fire and quick progress in the negotiations, which he described as having reached "a most sensitive stage."

"It is essential that the fighting stop and that the negotiations proceed in good faith," Speakes said.

The statement came amid a long and busy weekend and globe-girdling communications by U.S. officials struggling to stave off a full-scale Israeli attack.

Senior officials of the National Security Council and State Department spent much of the weekend in Lebanon-related meetings here and in California, where Reagan is vacationing. Speakes said Reagan is receiving frequent updates on the situation, particularly on efforts by special U.S. envoy Philip C. Habib and is responding in detail to points raised by Habib.

Outgoing Secretary of State Alexander M. Haig Jr. was also reported directly involved from the resort hotel where he is vacationing in West Virginia.

The U.S. efforts, officials said, centered on the twin goals mentioned by Speakes--maintaining the tenuous cease-fire and achieving progress in negotiations between the Palestine Liberation Organization and the Lebanese government on ending the armed Palestinian presence in and around Beirut.

One major strand of U.S. diplomacy was an appeal to Prime Minister Menachem Begin, in advance of Sunday's Israeli Cabinet meeting, to continue the cease-fire. The plea, forwarded by U.S. Ambassador Samuel Lewis late Saturday, took the position that movement in the Beirut talks justified additional efforts.

Administration officials said the duration of the new Israeli respite, granted at Sunday's meeting, is uncertain. The officials said, however, that Israeli impatience is unrelieved and that Begin's government appears closer to a decision to take new military action.

One report that could not be confirmed last night was that Reagan personally intervened with Begin to ease the pressure on Beirut.

One of the main U.S. efforts yesterday involved the tightened Israeli blockade of West Beirut and sharp restrictions on water and electricity there. These Israeli pressures brought strong protests from Lebanese authorities, who said they impeded the negotiations in practical and political ways.

A meeting late yesterday in Beirut between Habib and Israeli Defense Minister Ariel Sharon was believed to center on the Israeli pressures against Beirut.

Habib was also in touch with the PLO-Lebanese negotiations, which produced a written position for the first time Saturday by PLO Chairman Yassar Arafat. That agreement, while seen as a tangible landmark on a road to eventual settlement, left many issues unresolved.

The White House statement yesterday, the first substantial U.S. public statement this weekend, strongly suggested as much, saying, "The negotiations in Beirut are extremely complex with many issues and many parties involved."

The statement added, "The president believes there is a need for an early settlement because any delay raises the prospect of new fighting."

There were continuing indications that an outside military force is under consideration for a police and observer role in Beirut following a withdrawal by Palestinian guerrillas. U.S. officials declined to discuss the possible makeup of such a force and the possibility that U.S. troops might be involved.