Secretary of State Cyrus R. Vance will visit Egypt. Israel and other Middle Eastern nations Dec. 9 - 15 to encourage the spread of face-to-face peace talks, the State Department announced yesterday.

The Vance mission will try to build on the direct negotiations launched by Egyptian President Anwar Sadat and Israeli Prime Mininster Menachem Begin. Jordon, Lebanon, Saudi Arabia and Syria - if it agrees to see Vance - will be urged to support the process initiated by Sadat and Begin.

For its part, the Carter administration will be attempting to keep the negotiating process pointed toward its goal of "a comprehensive peace settlement" between Israel and all the Arab nations on its borders.

This represents a shift in U.S. strategy away from the focus on a Middle East conference in Geneva as the starting point of negotiations. Sadat and Begin already have moved beyong that objective, and U.S. strategy is now adapting.

The Vance mission will be "complementary and supportive of the Cairo conference due to begin about Dec. 14, said State Department spokesman Hodding Carter III.

Participants in that conference are Egypt and Israel as the principals, plus the United States and a United Nations observer. The conference is being avoided by the other invitees - the Soviet Union, Syria, Jordan, Lebanon and the Palestian Liberation Organization.

What the United States is doing through the Vance mission, said the State Department spokesman, "is seeking, however and wherever we can, to encourage all of the parties to stay on a path which can lead to a comprehensive a peace settlement."

"The President believes," the State Department said, "that in these circumstances the United States can support progress toward peace by continuing the exchange of views with Middle East leaders at the highest level which the administration has been conducting since January."

Administration officials said yesterday that the desire to keep the United States involved through the Vance mission in the dramatically shifting Middle East diplomacy was the main reason why it asked Sadat to postpone the start of the Cairo conference for about 10 days. Sadat and Israel's Begin both welcomed the idea for the Vance trip, officials said. News of the mission began leaking out of other capitals early yesterday before the U.S. annoncement.

Vance's trip will be added on to his long-scheduled visit to the NATO ministerial meeting in Brussels. Vance will leave Wednesday morning for Brussels, and is scheduled to travel to Cairo on Friday.

From Egypt, he will go to Israel, then Lebanon, briefly. His itinerary after that is unclear because of uncertainty about Syria's attitude, but Vance subsequently will visit Jordan and end his trip in Saudi Arabia on Dec. 14 and 15. Saudi Arabia, although not one of the Arab "confrontation states" in Arab-Israeli warfare, is the extremely influential financial backer of Egypt and many of other Arab nations.

Administration officials said that nothing they have seen out of the Tripoli conference of Arab opponents of Sadat's leapfrog diplomacy with Israel appears likely to influence Sadat's course.

Egypt's decision yesterday to sever diplomatic relations with Syria, along with other participants in the Tripoli conference, came as another of the many recent surprises to U.S. planners. Nevertheless, they said that at Tripoli Syria avoided extreme actions against Egypt, and that Syria may still agree to receive Vance to avoid cutting itself off completely from on-going Middle East diplomacy.

State Department spokesman Carter said the Vance mission "is not a negotiationg trip" and "we are not carrying U.S. prposals at all." Nor, he said, is it "an attempt to get Syria, stage," or even attempt to get Syria, Jordan and Lebanon "to change their minds at this point" about attending the Cairo conference.

Instead, he said, the trip is to explain U.S. objectives and its role in the Cairo conference, and to attempt to ascertain "what comes afterwards."

Beyond these generalizations, however, what is emerging is a basic shift in U.S. strategy - and rationalization - to adapt to the Sadat-Begin breakthrough, which is affecting the totally of Middle East diplomacy.

Sadat and Begin are describing their new affirmity as a foundation for developing a comprehensive Arab-Israeli settlement. What they are indicating is that their negotiations hopefully will produce the basis for an Egyptian-Israeli settlement, and the outlines of subsequent Israeli-Jordanian, Israeli-Lebanese and Israeli-Syrian peace settlements.

This was the original U.S. goal, administration officials maintain, and a Geneva conference as a starting point for negotiations was only projected as a way to begin the process. The United States is now happy to revert to the preferred, alternative approach, officials say, and when or whether it is confirmed at a Geneva conference is a very subordinate factor.

In its embrace of the new diplomatic direction, the administration also is saying that those who fail to join it may prove themselves "irrelevant" - and that includes, it is said, the Soviet Union and the PLO.

Under Secretary of State Philip C. Habib is in the Soviet Union, as a spokesman put it, "to exchange both projections and thoughts" about the new pattern of events in the Mid-east. Habib reportedly is telling the Soviet Union that the United States is disappointed in the Soviet role as co-chairman - with the United States - of the Geneva conference in exerting influence on its Arab clients to get that conference started. The Soviet Union was particularly expected to use its influence with Syria and the PLO.

The U.S. attitude is said to be that in the pattern now developing, Ameican interests can be much better protected in the Middle East than can Soviet interests. It is up to the Soviet Union to choose, it is said on the U.S. side, whether it will be left on the sidelines.

Similarity, an administration source says, the PLO "is in the process of making itself increasingly irrelevant to the mainstream of events" by its hostility to negotiations.