The Carter administration yesterday put an officially encouraging stamp of "progress" on what it termed the "concrete steps" taken by Egypt and Israel to move toward an overall Arab-Israel peace settlement.

At the same time, authoritative sources said the United States is intensifying its efforts to gain backing from moderate Arab nations to support Egyptian President Anwar Sadat's attempts to reach a compromise with Israeli Prime Minister Menahem Begin.

The outcome of the weekend Sadat-Begin talks in Ismailia, U.S. sources said, underscored the vital need for Sadat to demonstrate that he is not pursuing a separate Egytian-Israeli peace settlement. Sadat's insistence that he is opening a path for an ultimate 'Palestinian state' requires more sensitive response from Israel, and hopefully, support from Jordan and Saudi Arabia, these sources said.

The point on which the Sadat-Begin a U.S. source said, was on Israel's offer of "self-rule" for Palestinian Arabs in the Israeli-occupied West Bank of the Jordan River and in the Gaza Strip, with an Israeli military presence to remain in the two regions. Under the offer, this arrangement could be reviewed in five years.

Egypt's counter demand was for ultimate, assured "self-determination." which could permit a Palestinian state or any other arrangement desired by the 1 million Arabs involved. They are the major inhabitants of the regions, which include Israeli settlements. Begin balked at the Egyptian interpretation of "self-determination."

In a declaration obviously intended to counter disappointments about the inability of Sadat and Begin to overcome this central disagreement, the State Department stressed yesterday that "a process of negotiation" is now underway.

"It seems to us important at this point to maintain perspective on the meetings which have taken place," said the statement authorized by Secretary of State Cyrus R. Vance.

State Department spokesman Tom Reston told a questioner, "No, we're not disappointed," because he said, U.S. officials knew there could be no "instant peace overnight."

Administration officials now expect new attention to focus on American attempts to bring Jordan into the talks, and at a later stage, possibly Syria.

President Carter is scheduled to meet in Tehran next Saturday with Jordan's King Hussein, during Carter's six-nation trip abroad. In addition, the possibility continues to be held open for a Carter meeting with Syrian President Hafez Assad, in Riyablh, Saudi Arabia.

An administration source said "the suggestion has been passed to Assad - it has not been picked up."

Spokesman Reston said yesterday, "As the President Assad if it can be worked out. As of this time there are no plans for such a meeting."

What does trouble administration officials right now is what they regard as the unwarranted sense of setback in many quarters over the Sadat-Begin talks. This attitude is now providing a tempting target for the Arab "rejectionist front," and for the Soviet Union, to step up their attacks against the peace initiative launched last month by Sadat.

"We have always recognized," the State Department countered yesterday, "that the beginning of negotiations, while a crucial step, would not by itself resolve all of the difficult problems . . .

"We are pleased," the statement said, "that progress has been made at the recent meetings and that concrete steps have been agreed on for continuance of the substantive discussions."

It has been the U.S. objective, working with the Middle Eastern parties, it was said, "to establish a process of negotiation which could lead to comprehensive peace."

As 1977 ends, the statement said, "there are now direct negotiations dealing with the principles that would cover a comprehensive settlement and other substantive and procedural matters that would be part of an overall settlement."

Sadat and Begin share the same objective, the statement concluded, and "establishing a negotiating framework for a comprehensive settlement will be one of the important items on the agenda in the weeks ahead."

Secretary Vance "stands ready to do whatever will be helpful and supportative" in this process, the spokesman said, although no details are yet arranged.

Vance has been invited by Sadat and Begin to participate in the political committee that is scheduled to meet in Jerusalem in mid-January to grapple with the unresolved political subjects in the Ismailia talks.

Administration policymakers, spokesman Reston said, are still reviewing reports on the Sadat-Begin meeting, received yesterday from U.S. Ambassador Herman F. Eilts in Egypt and Samuel W. Lewis in Israel.