LUXOR, Egypt — Secretary of State Rice has persuaded Prime Minister Olmert of Israel and President Abbas of the Palestinian Authority to hold a three-way meeting sometime in the next month to discuss the “political horizon necessary to create a Palestinian state,” a senior State Department official traveling with Ms. Rice told reporters on her plane yesterday.

The meeting could signify progress in the long-stalled Israeli-Palestinian Arab peace negotiations.

The two sides are supposed to adhere to a three-stage, American-backed peace plan from 2003 known as the “road map,” which lays out a set of sequential steps, but the State Department official suggested that this meeting would allow the two leaders to begin to sketch out the parameters of a final deal.

He said the full details of the meeting were still to be worked out, including the exact date and location. He said Mr. Abbas in his meeting with Ms. Rice on Sunday had said he was comfortable talking about “the political horizon” with Mr. Olmert. Ms. Rice, in a meeting with Mr. Olmert yesterday, suggested that the three meet in the near future.

Ms. Rice met with Mr. Olmert yesterday morning and then arrived in Luxor for a meeting with President Mubarak of Egypt. She will then finish her day in Riyadh, Saudi Arabia, where she’s having dinner with King Abdullah of Jordan.

An Israeli government spokesman, David Baker, said it was an “agreement in principle” for a meeting but that there was no timeframe for when it would take place.

He said it was designed to “generate momentum” in the Israeli-Palestinian Arab peace talks.

Mr. Abbas said Sunday at a joint news conference in the West Bank with Ms. Rice that he adamantly rejects “any temporary or transitional solutions, including a state with temporary borders,” throwing cold water on an idea advanced by Israel’s foreign minister.

Ms. Rice is touring the Middle East this week in what she bills an effort to listen to ideas to rekindle the stalled peace talks. She has said she wants to “accelerate” the road map plan, but has been vague about what she means.

Ms. Rice has been hearing conflicting advice on her trip: The Israelis have advanced the idea of jumping to the second stage, an interim stage, and the Palestinian Arabs have pressed for going to the third stage, a permanent stage. Egypt and Jordan want to drop the road map and move immediately to “final status” talks, Foreign Minister Ahmed Aboul Gheit of Egypt said last week.

Ms. Rice has not tipped her hand about which approach she favors — or whether she has her own ideas. Referring to Mr. Abbas’s desire to skip the second stage envisioned in the road map, Ms. Rice said: “I’ve heard how he sees the road map and how to get to that end state. And so I think it’s not a bad thing to listen. But … it’s also important to act, and we’ll look for ways to act.”

Ms. Rice told reporters Sunday that she planned longer meetings with Arab and Israeli officials during this trip. She noted that this was her third trip to the region since October to discuss the Israeli-Palestinian Arab issue. She renewed her pledge to devote more effort to achieving peace.