The United States has mounted a diplomatic campaign with a wide array of countries in an effort to bring an end to the sudden surge of heavy fighting in Lebanon, Secretary of State Alexander M. Haig Jr. told Israeli leaders here today.

The U.S. efforts with Syria, the Soviet Union, France, the Vatican and other parties were made known and rising Israeli concern about the conflict between Lebanese Christian and Syrian forces in neighboring Lebanon, the most serious outbreak of fighting there since 1978.

Possibly in response to the U.S. pleas, Pope John Paul II called today for a halt in the fighting and said the Vatican has intervened to stop the week-long conflict.

Israel has expressed "deep concern" about the renewal of Christian-Syrian fighting, which could bring new tension and instability to an area repeatedly rent with warfare in the past. The Lebanese government, also contacted by the United States, has shown itself powerless to stop the fighting.

In a wider perspective, Haig's mission in a meeting near Cairo this morning with Egyptian President Anwar Sadat and another here this afternoon with Israeli Prime Minister Menachem Begin and his top ministers was a start on forming the regional "strategic consensus" to which Washington looks for improved security and diplomatic accord in the Middle East.

Haig found a ready welcome in both Egypt and Israel for a stronger U.S. role in the area to counter the Soviet Union. Sadat, for example, said approvingly after seeing Haig that "it is time that the United States resumes its role at the first superpower all over the world."

Israeli leaders, too, praised a more muscular U.S. role and were delighted with Haig's public declaration that "Israel has an important role to play in our common effort to safeguard our strategic interests in the region."

Haig did not spell out this role but an official in his party said it involved the strategic geographical location of the Jewish state as well as its highly rated military power and intelligence resources.

Haig was quickly confronted with evidence, however, that common interest on global strategic issues does not automatically erase political and military problems that have complicated U.S. policy in the region.

Egypt and Israel, for example, continue to have important differences on the makeup and operation of a multinational peacekeeping force, including some U.S. troops, which is proposed to police the part of the Sinai that Israel is scheduled to relinquish next April under the Camp David accords.

The differences are not irreconcilable, but will require further detailed discussions, patience and good will on both sides, U.S. officials said tonight.

Deputy Assistant Secretary of State Michael Sterner, who has been the chief negotiator in talks on the multinational force, is returning to Washington to redraft U.S. proposals, which were outlined in some detail by Haig in talks with Sadat and Begin, sources said.

Among the issues to be resolved is the question of Egyptian sovereignty within the Sinai zone where a peacekeeping force police are responsible for internal security, and would like acknowledgment of this in the ground rules for the multinational force. Israel is unhappy with this idea.

Israel has insisted that an effective unit of U.S. troops be included in a peacekeeping force to ensure that it could not be withdrawn suddenly under Egyptian or other Arab pressures in a moment of tension. The withdrawl of a U.N. peacekeeping force in 1967 was a factor in precipitating the Israeli-Egyptian war that year.

Egyptian negotiators have expressed willingness to accept U.S. forces ad a last resort if troops of other nations cannot be organized in sufficient numbers for the task.

U.S. officials, saying that Sadat expressed "flexibility" about aspects of the peacekeeping plan in today's meeting, said there is little doubt that some U.S. troops will be part of the Sinai force if Congress approves.

Sadat was reported to be relieved by a personal assurance from Haig that U.S. troops in a Sinai peacekeeping unit would be solely for the purpose of policing the area relinquished by Israel, and would have no role in orher Middle East conflicts and crises such as those in the Persian Gulf.

A formal limitation of the mission of the peacekeeping force, along these lines, has already been written into its proposed charter, U.S. officials said.

Sadat, speaking to reporters after the meeting with Haig, said, "We will be going to the United Nations" to ask U.N. sponsorship of a Sinai peacekeeping unit. But Egyptian as well as U.S. officials have all but conceded that U.N. sponsorship will be impossible, because of Arab opposition and a possible Soviet veto.

On another contentious question, Israeli leaders sharply criticized proposed U.S. aircraft sales to Saudi Arabia in the meeting with Haig, according to U.S. and Israeli sources.

Despite Haig's defense of the sales, which he described as a legacy of the Carter administration, Begin and the other leaders left little doubt of all-out Israeli opposition to the sale of radar-equipped AWACS (Airborne warning and command aircraft systems) to Saudi Arabia, as proposed by the Pentagon and expected to be approved by the Reagan administration.

The Israeli government had not taken an all-out lobbying stand in Washington against the proposed sale of F15 enhancement equipment to the Saudis. But Israeli officials argued that sale of the AWACS was even more serious, because it could more seriously erode the "technological edge" of Israel's Air Force over that of Arab states.

Haig has insisted before and repeated today that the United States is dedicated to maintaining the Israeli edge. But he reportedly did not offer today any additional compensatory measures to assure the Israelis on this point.

The Saudi sales issue aside, the tone of the talks here, as in Egypt, was described as positive by U.S. officials.