As the Jewish Sabbath ended at sundown yesterday, Israeli Prime Minister Menachem Begin telephoned Egyptian President Anwar Sadat to congratulate him on their shared Nobel Peace Prize and reaffirm his hope for peace.

In a press conference in the garden at his home, Begin, whose government created new difficulties in the peace negotiations last week by announcing that Jewish settlements in the West Bank would be expended, said he told Sada that the Nobel award is a "famous, great prize," but that the "real prize is peace itself." Begin added that Sadat agreed.

The Nobel selection committee announced that the Middle Eastern leaders were chosen for the award Friday, but Begin had remained secluded for the Sabbath.

Meanwhile, in his first comment on the award, Sadat said yesterday that he was dedicating his prize to the Egyptian people and to countries that supported his peace initiative with Israel.

"This award is to honor the entire Egyptian people for their struggle, determination and patience," Sadat said.

While most Western leaders hailed the selection of Sadat and Begin for their peace efforts, Arab reaction was generally negative.

In Damascus, Syria, a spokesman for the Palestine Liberation Organization said the award came "While Begin is still an aggressor against Palestinian land and rights and while Sadat is Begin's partner."

State-run Radio Damascus said, "It is not an honor for Sadat to share any prize with an anti-Arab terrorist like Menachem Begin."

In New York, Hasan A. Abdel Rahman, a deputy U.N. observer for the PLO, said the choice of Begin was "against the concept of peace and justice," but he did not comment on the selection of Sadat.

Soviet Foreign Minister Andrei Gromyko, in Paris for diplomatic talks, dismissed the awards as "a joke."

"Frankly, I think the award resembles a certain sort of joke," he said. "I think, however, not everybody shares that point of view."

The five-member Nobel committee said the award was to honor past actions and to "encourage further efforts to work out practical solutions" toward a Middle East peace.

While talking to reporters Begin said that during the brief conversation he reminded Sadat that 10 months ago the two had talked about the possibility of a Nobel prize once a peace treaty is signed, probably in the city of Beersheba. Begin mistakenly identified the city in which the prize is awarded as Stockholm rather than Oslo.

The anecdote is part of a transcript of the conversation released by Begin's office.

Begin: "Good evening Mr. President. I congratulate you on the award."

Sadat: "Mr. Prime Minister. I congratulate you."

Begin: Mr. President, do you remember when were in Ismailia I told you that Beersheba is on the way to Stockholm. You laughed very much. And now Mr. President, let our delegations resume their negotiations so that we can conclude the peace treaty and sign it and invite President Carter."

Sadat: "Yes, the vice president has already instructed our delegation to renew the negotiations with your delegation."

Begin: "Wonderful. We shall invite President Carter, of course, when we reach an agreement and can sign it."

Sadat: "Yes, for sure. President Carter, you know, is the unknown soldier in this process."

Begin: "Yes, of course, he deserves it absolutely. I hope to meet you at the time of the signing of the peace treaty. The real prize is peace itself."

Sadat: "Yes, I agree with you absolutely."

Begin: "Good night, Mr. President."

Sadat: "Good night, Mr. Prime Minister."