Secretary of State George P. Shultz began his search for renewed diplomatic momentum in the Middle East here today in a strategy session with U.S. emissaries and a midnight meeting with Saudi King Fahd. An aide to Shultz said that it would take "a miracle" to produce an immediate breakthrough in light of the prospects at hand.

Shultz arrived by U.S. Air Force plane early this afternoon from Pakistan, the final stop on a tour of East and South Asia, and was met by the Saudi foreign minister, Prince Saud, and other officials.

With Shultz at his elbow, Saud told reporters that the visit indicates "the United States is doing everything possible in order to achieve peace in the Middle East in general and in Lebanon in particular, which would lead to the withdrawal of Israeli troops from that country."

Saud later conferred privately with Shultz and then held a late-night meeting at a seaside palace with Fahd, who reportedly had been at prayer in nearby Mecca when Shultz arrived. Saudi Arabia and the rest of the Islamic world are observing the prayer and fast of Ramadan.

Shultz conferred for about two hours in a hotel-like royal guest house this afternoon with his traveling Middle East policy team, augmented by U.S. emissaries in the area. These include special envoys Philip C. Habib, Morris Draper and Richard Fairbanks. Also participating was U.S. Ambassador to Saudi Arabia Richard W. Murphy, who is an expert on the Arab world and a former U.S. ambassador to Syria.

While Shultz has been traveling through Asia for the past 10 days, the Habib team has been probing for diplomatic flexibility in visits to Jerusalem, Beirut and Jeddah. A participant in the meeting said the team believes a serious prospect exists for various maneuvers in those three capitals that could increase the pressures on Syria to withdraw its forces from Lebanon.

That prospect, however, was said to have been reduced by the recent Washington leak of a U.S. proposal that Israel set a "date certain" for withdrawal of its troops from Lebanon. U.S. sources here called the leak damaging and professed to be puzzled about why and by whom the disclosure had been made, in what they said was a distorted form.

Shultz's game plan, according to his aides, calls for assessment of the Saudi factor in his conference with Fahd, followed by a visit to Beirut during daylight hours Tuesday to see President Amin Gemayel and other officials. The main message there, officials said, will be one of continued U.S. support and reassurance for the Lebanese government.

Late Tuesday Shultz is to fly to Damascus, the crucial stop, for meetings with President Hafez Assad and his senior aides. The key question is whether the Syrian government, despite its hard-line public stance, is ready to approach negotiations with Lebanon on the withdrawal of its troops from that country.

Washington Post correspondent Herbert H. Denton reported from Beirut that an editorial Monday morning in Al Baath, the newspaper of Syria's ruling Baath Party asked, "Why is Shultz coming back to the Middle East?" The editorial added that if Shultz has returned to get Syria to accept the Lebanese-Israeli troop withdrawal agreement, "then this is an impossible mission."

State-run Damascus radio suggested that Shultz's efforts were intended to improve President Reagan's image for the presidential campaign. But it said, "Shultz will not resurrect the stillborn American-Israeli agreement, which they are trying to impose on Lebanon, but he will try to render a new service to expansionist, aggressive Israeli strategy."

In Moscow, the official news agency Tass said Shultz's Middle East trip "is aimed at compelling Arab countries to go along with the United States' military-expansionist plans" in the region, The Associated Press reported.

The assessment of the Habib team, sources said, is that recent Syrian action to split and dominate the Palestine Liberation Organization has increased the intransigence in Damascus by seeming to illustrate that tough action pays off. The U.S. officials have not given up hope, however, that Syria will see withdrawal of its troops from Lebanon as in its interest because only such action will bring about parallel Israeli withdrawal.

Shultz's personal probing in Damascus is considered particularly important in the absence of other high-level American contacts with Assad. Since Shultz's shuttle trip to the area two months ago, a trip that produced final agreement on an Israeli-Lebanese accord, the Syrian government has refused to accept visits from Habib.

Late Wednesday, following the conferences in Damascus, Shultz plans to fly to Israel to see Prime Minister Menachem Begin and other officials.

Increasing political pressure is reported in Israel for a partial troop withdrawal within Lebanon to a line that can be more easily defended without major casualties. Washington, which has opposed such a partial pullout on the ground that it could conceivably reduce the incentive to pull out completely, has been edging toward reluctant acceptance of such an Israeli move if it is done in coordination with other parties, especially Lebanon.

The current assessment among officials in Shultz's party is that Israel is unlikely to order a partial troop withdrawal without full consultation with Shultz. To do otherwise would be to court damage to the recently restored U.S.-Israeli relationship.

Here in Saudi Arabia, increasing concern is reported with the lack of momentum toward troop withdrawals from Lebanon since Shultz worked out the Israeli-Lebanese accord two months ago. According to a source close to the Saudi royal family, Habib was told here last week that no forward movement is likely until the United States decides what its course will be and moves vigorously to pursue it.

The Saudis are credited by senior members of Shultz's party with having made serious efforts to persuade the Syrians, who are longtime beneficiaries of Saudi financial support, to move toward withdrawal of Syrian forces from Lebanon as the only means to get the Israelis out.

The Syrians, however, have a long record of ignoring Saudi entreaties. This spring, for example, Crown Prince Abdullah, who has long been the key Saudi figure on Syrian affairs, made a visit to Damascus to plead for reopening of the oil pipeline from Iraq to permit the financially strapped Iraqis to sell more of their crude oil. The plea was ignored.

In recent days the Saudis dispatched another frequent and highly trusted emissary, Education Minister Abdullah Khuwaytir, to Syria with a plea for the restoration of unity in the PLO under the leadership of Chairman Yasser Arafat. So far as can be learned, Syria turned a deaf ear.