With a pledge to "bend their best efforts toward successful completion" of the deadlocked Middle East peace talks, high-ranking Israeli and Egyptian officials began meeting yesterday with Secretary of State Cyrus R. Vance in the snowbound seclusion of Camp David, Md.

Vance's meeting with Egyptian Prime Minister Mustapha Khalil and Israeli Foreign Minister Moshe Dayan marked the latest in a four-month series of U.S. mediation attempts to bring to reality the Egyptian-Israeli peace treaty whose principals were agreed upon at Camp David summit last September.

However, both Israel and Egypt are known to have returned to Camp David with the feeling that the new talks, even if they make progress, will not break the impasse completely and that another summit involving President Carter, Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin will be required.

However, U.S. officials have continued to express hope that, in the new talks sealed off from reporters, Vance may be able to make the breakthrough that eluded him during earlier negotiations in Washington and a Middle East shuttle mission in December.

At the meeting in the Catoctin Mountains 60 miles north of Washington, Vance is expected to present the two sides with new U.S. proposals for bridging the unresolved issues in the negotiations.

According to U.S. aides involved in planning the session, the tentative scenario calls for the three officials to discuss the proposals until Saturday or Sunday. Although no firm decisions have been made, there are some expectations that Carter will join the talks briefly on the weekend.

Then there will be a break while Dayan and Khalil report to their governments. Beyond that, the officials said, it is impossible now to predict whether they will return to Camp David for further talks with Vance or whether the three countries will discuss a new summit.

The main sticking point in the negotiations has involved Egypt's insistence that the peace treaty be accompanied by a timetable and target date for completing separate negotiations on establishing autonomy for the Palestinian inhabitants of the Israeli-occupied West Bank and Gaza Strip.

Sadat wants this so-called "linkage" to protect himself against charges in the Arab world that he is ignoring the interests of the Palestinians in order to achieve a separate peace with Israel. The Israelis, while saying they are willing to negotiate the autonomy issue as soon as a peace treaty is achieved, so far have refused to accept a timetable or a target date.

There also are major unresolved disputes over sections of the draft treaty text dealing with provisions for reopening the peace agreement to revision in the future and with the treaty's relationship to other Egyptian pacts.

A proposed U.S. draft, accepted by Israel, states that the treaty takes precedence over all other treaty obligations of Egypt and Israel. However, because of concern about his Arab world relations, Sadat has refused to accept language explicitly giving the peace treaty priority over his mutual defense pacts with other Arab states that might come into conflict with Israel.