Israeli Prime Minister Menachem Begin yesterday called for "the renewal of American understanding" for his peace proposals following two days of "difficult" talks with President Carter.

Begin's appeal, in a National Press Club appearance before departing for New York and then home, came amid new signs of an impasse between the United States and Israel on basic issues in the Middle East peace negotiations.

After a briefing from Carter at the White House, members of the Senate Foreign Relations Committee expressed deep discouragement about the prospects for the stalled Egyptian-Israeli negotiations in view of Begin's stands.

Later the White House announced that a planned official statement on the Carter-Begin talks - normally a routine diplomatic exercise - will not be issued because "the disagreement is abundantly clear" and repeating it "could complicate an already difficult situation."

White House press secretary Jody Powell denied as "without foundation" an Israeli radio report that Carter administration officials are seeking to force Begin from office. The radio report said that a senior American official had spoken to an Israeli leader in Washington of the "need to replace" Begin in the interest of the Egyptian-Israeli negotiations. No source or names were given.

Begin himself chuckled and grinned broadly when asked at the National Press Club whether he believes the Carter administration is trying to force him out. "No, I don't - but I would like to say that the prime minister of a democratic country is elected by the people of the country and only the people of the country," Begin replied.

The somber mood of American and Israeli officials, and the relatively subdued spirits of the 64-year-old Israeli political leader, left little doubt of serious concern on all sides on the morning after the unsuccessful Carter-Begin talks. Some American officials found consolation in the fact that important differences had been faced and acknowledged, rather than papered over. In their view, this was an essential first step toward an ultimate resolution.

Begin, in his press club appearance [WORD ILLEGIBLE] television interviews, hinted at possible new difficulties to come in the already strained Washington Jerusalem relations. He made a fervent defense of Israeli settlements in the occupied West Bank, which the United States has called "illegal" and 'obstacles to peace," and seemed to suggest that more such enclaves may be authorized.

"It is a perfect right of the Jews in the land of their forefathers to settle. It would be paradoxical if Jews have a right to live in Jaffa and Haifa and New York and Washington but do not have the right to live Bethlehem," he said. He added his belief that the Jewish enclaves are "perfectly legal and legitimate."

In a broadcast interview with ABC-television, Begin said he would consider the possibility of establishing new settlements after he returns home. "The deliberation depends on the cabinet," he said. In recent weeks the Begin government had temporarily halted the authorization of new enclaves on the West Bank until after the Carter-Begin talks.

Begin's press club speech, his major public address during his current trip, made only guarded and limited reference to the open disagreement which has developed with the Carter administration.

As in the past, Begin recounted his steps in bringing his own two-part peace plan to Washington last December, where it was publicly welcomed as a step in the right direction. Begin recalled that Carter called the Israeli plan "a long step forward" at the time and that Secretary of State Cyrus R. Vance termed it "a notable contribution."

"It is with deep sorrow that I have to tell you that, at a certain moment in recent weeks, those good words of the past suddenly disappeared from the lexicon . . . because, seemingly, there was objection from the other side," Begin declared. He said that "fairness and justice" demand a different U.S. posture, and at another point called for "the renewal of American understanding for the Israeli peace plan."

Explaining and defending his two-part proposal, Begin said:

His plan for "complete administrative autonomy" for Judes and Samaria (the Biblical names for the West Bank) and the Gaza strip would give Arabs there greater freedom to run their own lives than ever. Israel must retain "responsibility for security and public order" because otherwise armed bands of the Palestine Liberation Organization would sit on mountaintops there, menacing Israeli cities below.

Begin's refusal to agree to the broad principle of a negotiated withdrawal of Israeli forces from the West Bank is a current sticking point in the negotiations with Egypt and the most serious conflict with the United States. At the press club and television interviews be said Israel has "our own inttrpretation" of Council-Resolution 242, the territory-for-peace bargain that has been the framework for negotiations. But he avoided an explicit statement of his government's view that this bargain does not apply to the West Bank.

His "far reaching compromise proposal" for return of the Sinai to Egypt went beyond the position of previous Israeli governments. He charged Egypt with changing its position on the line of demilitarization in the area to be returned, and said that retention of Israeli settlements in the Sinai is essential to prevent "gun running [and] arms traffic" from Egyptian-controlled territory to the Gaza Strip.

"Let us renew the spirit of the Jerusalem and Ismailia meetings," Begin declared. He said Israel wants negotiations to "move ahead at a speedy pace" and is ready for renewed talks with Egypt.

Members of the Senate Foreign Relations Committee, briefed by Carter at the White House, were generally pessimistic about the immediate chances for renewal of the momentum which followed Egyptian President Anwar Sadat's dramatic visit to Jerusale last November.

"It is discouraging, it is disturbing, it is highly difficult, it looks very frustrating right now, but I do not believe the president believe it [the Sadat initistive] is dead," said Sen. Jacob K. Jivits (B-N.Y.). He said he urged Carter to persevere despite the difficulties.

Carter is "deeply concerned, no question about it, and really is turning to us now in Congress for advice and counsel, said Sen. Charles H. Percy (B-Ill). He does not now see a basis for getting [the negotiation] back on track with the present set of facts that he has." Percy said Begin's position seems to be a major step backward that would make the process "much more difficult."