Israeli Prime Minister Menachem Begin said today that the hopes for an Egyptian-Israeli peace treaty now rest with President Carter's ability to persuade Egyptian President Anwar Sadat to accept the latest American peace proposals.

Only hours after Carter left Washington for Cairo, Begin told about 2,000 members of American-Jewish organizations here:

"May I say that we did our share. They are new proposals They restore the peace treaty to be a serous document. Indeed, now if the president convinces President Sadat that he too should give his approval, then very soon we will be signing a peace treaty between Israel and Egypt."

Begin coupled that assessment with a call for increased U.S. support for Israel, warning, as he has done repeatedly since arriving in the United States last week, that turmoil in the Middle East and elsewhere threatens. American interests.

Ticking off the names of a halfdozen strategic countries he said have fallen under the domination of the Soviet Union in the last two years, the prime minister warned his audience, "Liberty is in danger."

"If the Free World, and the United States as the leader of the Free World, has one reliable, stable all in the Middle East, its name is Israel," he said.

"We can defend liberty," Begin added. "But Israel should be strengthened, not weakened. Do what you can to bring about the quick -- as quick as possible -- strengthening of Israel. It's in your own interest."

Begin did not specify how he expects the United States to strengthen Israel, but this would presumably include massive new amounts of military and economic aid, which Carter has indicated he is willing to provide to both Israel and Egypt as part of a peace treaty package.

The Israeli prime minister's hourlong speech, liberally sprinkled with Yiddish sayings, was enthusiastically received by his audience and praised by officials of the Conference of Presidents of Major American-Jewish Organizations, which sponsored the event.

"I don't think he made a single statement that went beyond what was agreed to," said Benjamin R. Epstein, national director of the Anti-Defamation League of B'nai B'rith.

Epstein was referring to the fears among some Jewish leaders that careless, bellicose remarks by Begin here could undermine Carter's effort to sell Sadat on the latest American peace proposals, approved earlier this week by the Israeli cabinet.

But Begin was careful not to make controversial remarks in the speech, while making it clear that Israel considersthe fate of the tortuous peace negotiations now to rest directly on Sadat and indirectly on Carter.

"At this stage, I cannot tell you all that I know, because we are at a very delicate moment," Begin said today. "Yesterday, for the first time, President Sadat of Egypt heard about the American proposals.... The president [Carter] has to convince Egypt's leader and his advisers that he should also take a positive attitude toward these proposals."

Begin devoted the bulk of his speech to a defense of his description of the draft treaty as a "sham document" before the last-minute American suggestions for changes were made.

He said the earlier version would have allowed Egypt to cancel the treaty provisions if a comprehensive peace accord is not reached with other Arab nations, and to attack Israel with legal impunity if there is renewed fighting in the Middle East.

"Tell me, should we, could we have signed such [a] document?" He said, "Don't answer, I'll do it for you. We couldn't, we shouldn't, we didn't."