President Carter and Israeli Prime Minister Menachem Begin, meeting here for two hours yesterday, made no apparent progress toward a resolution of the fundamental issues that have stalled progress toward a Middle East peace agreement.

A White House statement said only that the two leaders had "a thorough discussion on the issues that must be resolved in order to assure continuity and progress inn the peace negotations." Informed U.S. sources said there had been "no movement" on either side, and described this opening round of talks as a recapitulation of existing policies and problems.

U.S. and Israeli officials pointed out that Carter and Begin would have the chance to discuss their differences at an intimate dinner, with only themselves and their wives Present, scheduled for last night, and at a final business meeting this morning.

According to congressional sources, Begin encountered unusually skeptical and sometimes critical questioning in separate closed meetings yesterday afternoon with the Senate Foreign Relations Committee and the House International Relations Committee. Lawmakers on both sides of the Capitol said the atmosphere was much less friendly than at similar sessions during Begin's two previous visits to Washington as prime minister.

"I'm not sure that he sensed that there was a roomful of friends who were reaching out for answers, and I'm not sure that he sensed that they didn't get them. A number of members felt that it was less than a howling success," said a senator, usually supportive of Israel, who asked not to be named.

A House member who has also supported Israel on many issues said congressional concern was expressed about Israeli settlements in occupied territories and described Begin's response as "Intransigent."

Another lawmaker said there was "a lot of muttering" by House members about Begin's remarks and that "questions were harder this time than they have ever been before."

Sen. Charles H. Percy (R-I11.) said after hearing Begin that he is engaged in "the toughest single negotiation that a prime minister of Israel has ever held with a president of the United States." Percy said that senators told Begin that Israel's insistence on keeping Jewish settlements in occupied areas "has divided Israel, divided the American Jewish community and caused an erosion of support for Israel."

Israel's invasion of southern Leabnon and U.N. efforts to arrange the withdrawal of Israeli troops and their replacement by U.N. peacekeeping force were not discussed at the White House business session, officials said. The United States had informed Israel in advance that the White House talks should center on such diplomatic problems as Israeli withdrawal from the occupied West Bank and Gaza Strip and potential Palestinian entity in that area.

The lack of agreement on a statement of principles covering these points is considered the most serious roadblock to further movement in the Egyptian-Israeli negotiations.

Welcoming his visitor in a simple ceremony on the South Lawn, Carter touched briefly on the search for peace taking place "for 10 years under the broad scope of United Nations Resolution 242." A disagreement over whether this requires Israeli withdrawal from the West Bank is a central issue in the current talks.

Carter called Begin "a man of destiny", and said the future of Israel and the Middle East rests on his shoulders. The President seemed to hint that Begin can afford to be flexible, saying that Israel is milttariy stronger than ever before in history."

"Peace can come from a guarantee of security, and our staunch friendship for Israel will continue to be a major element in this foundation for progress," Carter said Aides interpreted his mention of guaranteed security as a statement of existing U.S. policy rather than a suggestion of a new American proposal.

Referring to the soaring hopes for a quick peace agreement that followed Egyptian President Anwar Sadat's trip to Jerusalem in November, Carter declared that "those bright days of new opportunity have now been clouded over." He added that "the recent cowardly and injustified attack by terrorists on innocent civillians in Israel has resulted in the loss of hundreds of lives and tens of thousand of people who are now homeless."

U.S. officials yesterday estimated the death toll in the Lebanon fighting to be at least 700. On Capitol Hill, Sen. James Abourezk (D-S.D.), the Senate's only member of Arab ancestry, called the Israeli military action =imperialism" and charged it "goes beyond retaliation."

Begin's response to Carter at the White House welcoming ceremony came less than 30 minutes before Israel's cease-fire in Lebanon was to take effect. Begin made no reference to the action but, in a reference to the terrorist raid preceding it, said that "only 10 days ago Israel got another reminder of what character is the implacable enemy she faces, what is its designs and methods toward men, women and children, citizens of our country."