Secretary of State Cyrus R. Vance, declaring that he aims to speed up progress toward a Geneva peace conference, opened a new round of Middle East diplomacy here tonight in talks with the most flexible Arab leader.

Arriving to meet President Anwar Sadat at Sadat's beachfront villa outside this historic city, Vance praised the Eygptian as a great leader and statesman. Vance and his party have made no secret of their belief that Sadat's cooperation and flexibility are crucial to any possible peace talks and agreements with Israel.

Concerning the major stumbling block to a geneva conference, Sadat has suggested several ways that a Palestinian presence at the conference might be made less offensive to Israel and has repeatedly said the problem can be surmounted if Israel really wants peace.

Reporters aboard Vance's plane, in background talks with a senior official, received the impression that Vance hopes to work out a feasible formula for Palestinian representation in talks here with Sadat and then obtain agreement of leaders in the other Arab states along his route - Syria, Jordan, Saudi Arabia and Lebanon.

Then on the Final stop, if all goes well. Vance would be in position to present a compromise Arab plan or plans to Israeli Prime Minister Menachem Begin and hope for some matching flexibility on Begin's part.

During his recent Washington visit, Begin said publicly - and evidently privately as well - that Israel will accept palestinians at Geneva as part of the Jordanian delegation but will not agree to the participation of any known member of the Palestine Liberation Orgainzation.

The Arabs are believed unlikely to accept Begin's near-total ban on PLO participation. Vance's job is to find a formula acceptable to both sides in order to make a Geneva meeting possible.

Vance's demeanor as his mission began was one of guarded optimism. He has said several times that it might not be possible to finish working out the procedures leading to a Geneva conference during his 12-day trip.

Sadat, the Arab world's most persisdent advocate of a Geneva meeting and a man whose internal prestige depends on progress toward peace, allowed himself greater public hope.

"I'm more than optimistic," he told reporters as he sat down to the first session of talks with Vance.

Vance's talks with Sadat today lasted three hours, twice the scheduled time.

Vance planned talks Tuesday with Egyptian Foreign Minister Ismail Fahmi and a second, more detailed, meeting with Sadat Tuesday night.

News services reported the following

Arab newspapers greeted Vance's peace mission with a mixture of hope and skepticism, making clear that war is the consequence of failure in the talks.

In Egypt, the semi-official Cairo daily Al Ahram said the "Arab countries will never put obstacles in the way of Vance, who is coming is search of peace."

The newspaper added, however. "If the peace march fails, there would be no alternative left to total confrontation" with Israel.

Another Cairo daily, Al Akhbar, said Vance's visit will be "a decisive trip and (will bring) confrontation with the inescapable truth, either peace or war."

In Damascus, the government controlled daily Al Baathe deplored what it said was Vance's "new plan" to substitute moderate Palestinians for the Palestine Liberation Organization at future Geneva peace talks.

THe newspaper said Syria would discuss whatever proposals Vance brought, "provided they call for total Israeli withdrawal from occupied Arab lands, recognition of the rights of the Palestinians to establish their own independent state and PLO participation in peace negotations."

Al Baath earlier noted, "The settlement does not depend on the U.S. alone," a reminder that Syria remains on good terms with the Soviet Union, co-chairman with the United States of the Geneva conference.