"The more ground we have, the better," Barak said during a break in more than three hours of talks with Albright. It was the start of a three-day Middle East trip by Albright that will include a meeting with Syria's foreign minister.
Barak also suggested he was inclined to sweeten his territorial offers to the Palestinians in a drive to conclude a final accord over such sensitive problems as Jerusalem's future and how much land Yasser Arafat will have for his Palestinian state.
Elaborating on the settlers issue in a televised interview, however, Barak said it would be a historic achievement if he could reach an agreement with Arafat that keeps 150,000 of the 200,000 Jewish settlers on the West Bank.
Barak also accused Arafat of "a certain amount of foot-dragging" in the prolonged and tedious negotiations.
Albright held two meetings with Barak, interspersed with a working dinner at his home, and plans another session Tuesday night.
"We heard very clearly Prime Minister Barak's commitment to an agreement, and the discussions focused on how to get there," State Department spokesman Richard Boucher said.
Quizzed at a news conference about reports that he had determined retention of the Jordan Valley was no longer essential for Israel's security, the former Army chief of staff said a land-for-peace trade-off is complicated. He said it is too early to talk about areas Israel intends to keep.
"Basically, we need security and a settlement presence along the Jordan Valley," Barak said, "but the details can be decided only through negotiations."
Albright aims to set up a three-way summit for President Clinton with Barak and Arafat and to prod the two leaders toward agreement by their promised deadline of mid-September.
Albright, who accompanied Clinton on his trip to Russia, passed up his stop in Ukraine to follow up on a meeting between the president and Barak last week in Portugal and Clinton's telephone talk from there with Arafat.
Since then, Barak has offered to dismantle settlements containing up to 60,000 Jewish settlers as part of a peace deal.
On Monday, Haim Ramon, a close Barak aide who is minister for Jerusalem affairs, told Israel's parliament the Knesset: Most of the residents of the West Bank will be concentrated in settlement blocs. We said most of the settlers not most of the settlements.
Barak has already virtually conceded establishment of a Palestinian state.
Clinton administration officials, meanwhile, have urged on Barak and Arafat, but insist they are not making separate American proposals to cut through the impasse.
"We are there, ready to roll up our sleeves," Abright told reporters at the prime minister's office. "There really is a historic opportunity, and we have to pursue it full speed."
Overall, the concessions could involve Israel's surrender of about 93 percent of the West Bank, coming closer to Arafat's initial demand for a state on 99 percent of the territory Israel won from Jordan in the 1967 Six-Day War.
A senior U.S. official, traveling with Albright to Israel from Moscow, said her aim was to determine "what can and what cannot be done" by Barak and Arafat and to make preparations for a summit.
The official, speaking on condition of anonymity, said to expect at least one more trip by Albright to the region before any meeting involving Clinton, Barak and Arafat.
Even then, the official said, there would still be a gap between the two sides' positions. He said none of the major issues -- the future of Jerusalem, the amount of land to be taken over by the Palestinians and compensation for refugees -- has been resolved.
At Albright's request, Syrian Foreign Minister Farouk al-Sharaa agreed to meet with her Wednesday in Cairo. He will be in the Egyptian capital with several other Arab foreign ministers for a conference. Albright also will see Foreign Minister Youssef bin Alawi of Oman and President Hosni Mubarak and Foreign Minister Amr Moussa of Egypt.
She and Arafat are scheduled to meet Tuesday in Ramallah, on the West Bank.
In the meantime, Clinton is meeting in Washington on Tuesday with King Abdullah of Jordan. If Israel turns over Jordan Valley territory to the Palestinians, it could have an impact on Jordan's security. The majority of Jordanians are Palestinian.
Negotiations between Israel and Syria broke down in January over whether Israel would give up land all the way to the Sea of Galilee in returning the Golan Heights to Syria. Israel won the strategic high ground in the 1967 war.
The senior U.S. official said the door to negotiations remains open, but he gave no indication the talks would be resumed.