Egyptain President Anwar Sadat, in talks with President Reagan, yesterday called on the United States to inaugurate a new stage in the Middle East peace process by establishing contact with the Palestine Liberation Organization.

Sadat's plea, which came near the start of Reagan's first meeting with a senior Middle East leader on the future of the strategic and strife_torn region, broght no immediate response from Reagan.

Only hours before the White House session, however, Secretary of State Slexander M. Haig Jr. reiterated in a television interview the "very clear" and longstanding U.S. posture of rejecting a diplomatic role for the PLO until that organization recognizes Israel's right to exist.

Reagan and Sadat, in their public exchange of remarks during a ceremony of welcome and in their private White House conversations, pledged their determination to advance the peace process that emerged from the Camp David meetings of Egypt and Israel under the sponsorship of President Carter three years ago next month.

According to a White House briefing, Reagan initially did not outline his ideas about the next steps, deferring instead to his visitor in nearly two hours of official meetings.

Sadat's view, according to Egyptian sources, is that PLO acceptence of the recent U.S.-sponsored cease-fire in Lebanon marks a turning point in Palestinian acceptance of peaceful solutions with Israel. Sadat believes, the sources said, that the PLO action deserves an American response that could in turn encourage future moderation.

Sadat told reporters yesterday afternoon had he told Reagan, "It is not asking too much for the U.S. to continue to build on" the cease-fire. Specially, Sadat said, the United States should "drop the condition" of the 1975 pledge to Israel by then-secretary of state Henry A. Kissinger "which prevents the United States from contacting the PLO."

In the meeting with Reagan, according to a participant, Sadat made the point in indirect but unmistakable fashion by quoting his public appeal at a London news conference Tuesday for direct U.S. contact with the PLO.

One means of making contact with the PLO without an open reversal of U.S. policy, Sadat reportedly suggested at the White House, is through intensified American discussions with Palestinian mayors and other leaders on the Israeli-occupied West Bank of the Jordan River. Many of them are known to be PLO members.

Sadat also said that the Saudi Arabian role in helping to arrange the cease-fire in Lebanon was "significant" and should be encouraged, according to participants in the White House meetings. Sadat's remarks apparently reflect some improvement in the hostile and even bitter climate of Egyptian-Saudi relations since Camp David, and may presage further rapprochement.

Sadat, according to the sources, did not come here demanding or expecting immediate U.S. action to advance the peace process.

Sadat is said to have expressed his understanding of Reagan's need to consult fully with Israeli Prime Minister Menachem Begin, who is due here Sept. 9-10, as well as King Houssein of Jordan and Crown Prince Fahd of Saudi Arabia, who are expected later this fall.

Sadat plans to see Begin this month or next in the Middle East. At the White House yesterday, he suggested that "perhaps there could be, at some future date, another summit meeting" of Egypt and Israel involving the U.S. president, according to the White House briefing.

Sadat added that this would require "intense preparation," which remark was taken as a hint that the summit should follow the U.S. consultations with all the Mideast leaders.

Reagan, in his remarks of welcome on the steamy White House lawn, went out of his way to praise Sadat on a historic figure who is "one of the 20th century's most courageous peacemakers." Three times Reagan repeated, addressing those who have doubts about peace in the Middle East, "President Sadat has shown the way."

"We want you to know that although the Americans have changed presidents, we have not altered our commitment to peace or our desire to continue building on the achievements of Camp David," Reagan said.

Sadat responded that, "We are equally committed to the cause of peace."

Praising Reagan as "a man of faith and determination," Sadat said their talks come "at a crucial moment" because of "the rising tension and violence" of recent weeks in the Middle East.

The meeting was the first between the two men and, by all reports, was a warm one.