President Carter and Israeli Prime Minister Menachem Begin continued their critical talks on he Middle East yesterday without making any progress toward breaking the impasse that has threatened the chances for an Egyptian-Israeli peace treaty.

During 4 1/2 hours of meetings spread over Thursday night and yesterday, it was learned, the two leaders failed to find any common ground for overcoming the differences between Israel and the government of Egyptian President Anwar Sadat.

It is too early to tell where the talks, which are expected to run through Sunday, will lead, reporters were told. But, as of last night, it was known that nothing had happened to alleviate the sense of crisis underlying Begin's hastily arranged trip here.

The talks were set up after Begin rejected Carter's bid for a new toplevel Camp David meeting. The aim would have been to try and thresh out the disputes blocking realization of the treaty agreed to in principle by Begin and Sadat under Carter's mediation at the first Camp David summit last September.

The Israelis spurned the summit invitation because Sadat had planned to send a deputy rather than attend himself and because Begin believes that the Carter administration is trying to pressure Israel into major concessions demanded by Egypt.

Despite U.S. denials of strong-arm tactics and pleas that the disagreements not be idscussed in public, Begin arrived Thursday night defiantly warning that he will not be pressed into signing a "sham" treatly and describing the negotiations as in "deep crisis."

His apparent aim was to take his case over Carter's head to the American public. But, after delivering his initial message in an extraordinarily blunt manner, Begin shifted gears significantly yesterday.

His rhetoric in public was toned down considerably, and the Israeli delegation began to cooperate scrupulously in U.S. efforts to put a tight blanket of secrecy over the talks.

Although neithe side would say anything about the substance of the discussions, both seemed to be making a conscious effort to cast the talks in a hopeful light. A joint statement described a 2 1/2-hour meeting yesterday morning as "serious, wide-ranging and useful" and said it was conducted "in an atmosphere of friendship and candor."

Carter, who canceled an appearance at a Democratic fund-raising dinner in Los Angeles to meet with Begin, sent the gathering a videotape characterizing the Middle East peace process in optimistic terms.

"We now have come within inches of reaching a final agreement between Israel and Egypt," he said on the taped message. "I am determined to carry on this effort."

In addition to the morning White House meeting, Begin had a working lunch with Secretary of State Cyrus R. Vance at the State Department. But another White House session, tentatively scheduled for the afternoon, was canceled.

Spokesmen for both sides insisted that the cancellation was due to the facts that the morning meeting had run longer than expected, that there were no subjects requiring immediate attention in the afternoon, and that Begin wanted to prepare for a Jewish Sabbath evening dinner that he gave for Carter at Blair House last night.

Because of the sabbath, the talks will go into suspension today. But they are scheduled to resume after the sabbath ends at sundown with another meeting between Carter and Begin at the White House tonight.

The most important disagreement involves Egypt's insistence that the treaty be linked to a target date for completing separate negotiations on establishing Palestinian autonomy in the Israeli-occupied West Bank and Gaza Strip. Although U.S. officials insist that Washington will not object to any solution agreeable to the two sides, the United States is understood to be recommending that there be a one-year target for completiing the autonomy talks.

Egypt also has objected to a provision in the draft treaty that would give the agreement priority over Egypt's mutual defense pacts with other Arab states. The United States has suggested a clarification citing a nation's right to engage in collective self-defense under the United Nations charter, but Israel has continued to insist that any interpreatations cannot negate the treaty's primacy.

In addition, the United States has suggested that Israel go along with Sadat's reluctance to exchange ambassadors with Israel until Israeli withdrawal from the Sinai peninsula is completed and progress is made toward Palestinian autonomy in either Gaza or the West Bank.