The United States and Egypt agreed yesterday that hopes for a quick resumption of the stalled Middle East peace talks depend on Israel's response to recent proposals made by Egyptian President Anwar Sadat.

Sadat is expected to receive a reply from Israeli Prime Minister Menachem Begin today, and both Secretary of State Cyrus R. Vance and Egyptian Prime Minister Mustafa Khalil, who concluded four days of talks here yesterday, said that will determine what happens next.

Following a farewell call on Khalil at his hotel, Vance said: "All parties agree that the talks should be resumed. The question is when it will be useful to resume the negotiations. The first step that has to be taken there is to see what the answer of Begin is."

Although details of the Israeli response are not known, reports from Jerusalem on Sunday said Begin had submitted to his ministers a draft reply in which Israel agrees to resume talks on so-called "side letters" to accompany a peace treaty but refuses to reopen key issues already accepted by Israel for inclusion in the treaty text.

Earlier, Israel had accepted a draft treaty package proposed by the United States except for one major element.The Israelis rejected the idea of the treaty being accompanied by a specific timetable for negotiations to achieve Palestinian autonomy in the Israeli-occupied West Bank and Gaza Strip.

However, Sadat, spurred by concern in the Arab world about the Palestinian issue, countered by insisting on a timetable or, failing that, a target date for reaching an accord on the Palestinian autonomy question.

In his newest proposals, Sadat also is seeking to water down or eliminate an article in the U.S.-proposed draft that would give the Egyptian-Israeli treaty precedence over Egypt's other treaty obligations to assist its Arab allies in the event of a war with Israel.