Amid signs of a new effort to get the stalled Middle East peace talks moving again, Egyptian Prime Minister Mustafa Khalil conferred with Secretary of State Cyrus R. Vance yesterday, and then postponed his departure from Washington until tomorrow.

Khalil, who met with President Carter for three hours Friday to explain President Anwar Sadat's thinking on an Egyptian-Israeli peace treaty, had been scheduled to leave Washington yesterday for Romania and the start of a week-long European tour.

His sudden change of plans, announced after a two-hour session with Vance, appeared to reflect mutual agreement that he should be available for further talks with U.S. officials after the Israeli cabinet meets today to discuss Sadat's latest treaty proposals.

In a brief talk with reporters after the meeting, Khalil said he was staying because "I would like to continue the discussions with Mr. Vance." He acknowledged that Egypt "would like to see the negotiations resumed," but added that no decisions had been made on when or where the U.S.-mediated talks might get moving again.

The answer is likely to become clear after Israeli Prime Minister Menachem Begin's cabinet decides on its response to the ideas outlined by Sadat in separate letters to Begin and Carter.

The Washington talks have been suspended for almost three weeks because of Israeli and Egyptian differences over a proposed U.S. draft of the peace treaty.The Israelis have said they will accept the draft except for one key element in the proposed treaty package.

They refused to agree to an accompanying letter that would spell out a timetable for negotiations to establish limited Palestinaian autonomy in the Israeli-occupied West Bank and Gaza Strip. In announcing that decision, the Israelis originally said it was not subject to further negotiation.

However, that position is unacceptable to Sadat, who is anxious to protect himself against charges of making a separate peace with Israel at the expense of the Palestinians and the rest of the Arab world.

According to reliable sources, his latest proposals, as outlined in the messages to Carter and Begin, still seek to establish a link between an Egyptian-Israeli accord and the issue of Palestinian autonomy through a timetable, or, failing that, agreement on a target date for moving toward Palestinian self rule.

Sadat also wants to eliminate or substantially revise article six of the proposed treaty draft. It states that the treaty supersedes Egypt's other obligations -- a provision that would bar Egypt from entering any armed clash between Israel and other Arab countries.

Vance said Friday that the Israelis, despite their previous take-it-or-leave-it stance, "have said that at such time as it is useful to resume the negotiations, they will do so."

But if the Israelis reject Sadat's newest proposals outright, there apparently would be nothing to negotiate about.For that reason, the next step in the drive to get the talks moving again will depend on what the Israeli cabinet does today.

Also taking part in yesterday's meeting at the State Department was Vice President Mondale -- a factor that fueled speculation about his possibly playing a role in some dramatic U.S. initiative to revive the talks.

There has been speculation that Mondale, who has close ties to many Israeli leaders, might go to the Middle East or that he might temporarily assume command of the talks while Vance is in Europe attending a NATO meeting.

However, U.S. officials consistently have said there are no plans for Mondale, Vance or any other high-level officials to visit the Middle East. They said Mondale attended yesterday's meeting as a representative of the president and because of his strong interest in the Middle East situation.

After their morning session, Vance and Khalil met again for an hour at the Egyptian's hotel in what a U.S. spokesman described as "a continuation of their discussions." The spokesman added that the two had agreed to "keep in touch" over the weekend.