President Carter declared unqualified support yesterday for the continuing Egyptian-Israeli peace initiative and urged other nations to join the endeavor or at least not obstruct it.

Carter lauded Egyptian President Anwar Sadat and Israeli Prime Minister Menahem Begin for pursuing their peace efforts from their "historic breakthrough" meeting in Israel last month to new talks in Cairo.

The Cairo meeting, in which the United States will be one of the lonely participants along with Egypt, Israel and a United Nations observer, is "a very constructive step," Carter said. He urged Syria, Jordan and Lebanon, which will not attended, to "join in these discussions" later.

Carter disclosed that the Cairo talks will take about Dec. 13, later than anticipated, and that the United States will be represented by Alfred I., Atherton Jr., 56, assistant secretary of state for Near Eastern and South Asian affairs, a career diplomat.

The President's enthusiastic comments about the Egyptian-Israeli plunge into peace talks, which has split the Arab world, came at a televised news conference. They ended a five-day period during which the administration has been sharply criticized for hesitation and equivocation on Sadat's call for preliminary talks in Cairo among all participants in a reconvened Geneva conference on the Middle East.

Carter said that ever since "we discovered" that Sadat was going to Israel, the United States used its influence "to encourage the other nations not to condemn President Sadat."

He said. "This particularly applied to Saudi Arabia, to Jordan, to the European countries, to the Soviet Union," the co-chairman with the United States for a Geneva conference, "and to Syria," Carter said. "In some instances, either they decided not to condemn him or our influence was successful."

Subsequently, Carter said, the United States sought to rally support for the negotiations that now "will continue from Jerusalem into Cairo and also to avoid any condemnation of Sadat that might disrupt his influence and put an obstacle to peace in the future."

Although the United States was widely suspected of hesitating over the Cairo meeting because it feared that those talks were headed toward a separate Egyptian-Israeli peace settlement, Carter denied that.

'We and Egypt and Israel,' he said, "have all taken the position, publicly, and the same position privately among ourselves, that a separate peace agreement between Egypt and Israel to the exclusion of the other parties is not desirable."

If it becomes apparent at some later date, Carter said, that Syria, Jordan and Lebanon, the other potential participants at a Geneva conference along with the Soviet Union and Palestinian representatives, do "not want peace" with Israel, "then an alternative might have to be pursued. But we certainly have not reached that point yet."

Actually, Israel has said it would be prepared for a separate peace with Egypt, and Israeli Foreign Minister Moshe Dayan repeated that yesterday in West Germany, but that Sadat has declined that. Sadat has said the same thing.

"The road to peace" from Jerusalem to Cairo. Carter said, will go "ultimately we believe to a comprehensive settlement at Geneva."

Carter vigorously defended Egypt's Sadat, who has been attacked as "a traitor" by some of the most militant Arabs. Sadat has "evoked very clearly the basic Arab position." Carter said, "concerning Israeli withdrawal from occupied territories and also the resolution of the Palestinian question."

As for the Soviet Union, which has declined to attend the Cairo talks, Carter said that "in the past . . . the Soviets have not played a constructive role in many instances because they had espoused almost completely the more adamant Arab position."

However, "in recent months," Carter said, "the Soviets have moved toward a much more balanced position, as a prelude to the Geneva conference." The United States and the Soviet Union "disagree in some instances" on "procedural items" for Geneva, Carter said. He said he wished the Soviets had decided to go to Cairo.

Carter said that in Cairo, "we will make as much progress as we can following the leadership of Sadat and Begin." His belief, he said, is that the world desire for peace is so strong that ultimately "the Soviets will follow along and take advantage of any constructive step toward peace."

It was learned that one reason for the delayed Cairo meeting, which Sadat's invitations said would be held "at a date to be agreed upon starting Dec. 3," was a U.S. attempt to induce the Soviet Union to at least let its ambassador to Egypt sit in on the talks.

The United States had suggested that the U.S. ambassador in Cairo, Hermann Eilts, and the Soviet ambassador, could represent their respective nations. The Carter administration asked Sadat for a week to 10 days of additional time to try to work out participation of the Soviet Union and other nations, and Sadat readily agreed, U.S. sources said.

But the Soviet Union balked, along with Syria, and the Soviet-supported Palestine Liberation Organization which bitterly attacked Sadat's trip to Jerusalem and the Cairo talks.

Jordan and Lebanon, caught in the middle between Arab moderates and militants, straddled the divide. They said they would attend the Cairo talks and a conference called in Tripoli today by Sadat's severest Arab critics, if all parties attended either meeting, knowing that was ruled out.

President Carter left the United States uncommitted and unenthusiastic yesterday about an attempt led by U.N. Secretary General Kurt Waldhelm to bridge the split over the Cairo meeting by proposing, on Tuesday, a pre-Geneva conference at the U.N. after the Cairo talks.

Under Waldheim's proposal, discussed in advance with the United States and the Soviet Union, the same parties that Sadat invited to Cairo, including the PLO, would be invited to the United Nations.

Israel roundly rejected Weldheim's proposal yesterday, Carter noted, and said "it is too early for us to decide whether or not we will go to any conference if one is actually held at the United Nations."

The prospects are remote after Israel's opposition, diplomats said yesterday. A State Department spokesman said "we are not taking an active role in seeking to further or to block" Waldheim's proposal, and will be guided in part by other nations' attitudes.

The President's elaborate support yesterday of the Sadat-Begin talks, and his expressed optimism that the intense controversy about them will dissolve, encouraged speculation at least in Israel that Carter may visit Middle Eastern capitals in January at the end of his currently planned trip abroad. Israeli television broadcast that speculation yesterday.

Inevitably, Carter administration spokesmen said there are "no plans" for such a vist. Carter wants to visit the Middle East at some point, administration sources said, but at this stage no one can predict what will come out of the Cairo talks or what the diplomatic scene will look like in January.

Although the President said yesterday that Atherton will represent "high level" participation in the Cairo talks, the talks actually are at what the State Department has called "the expert level."