Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas made "significant progress on the issue of borders" during the meeting in Jerusalem on Monday, Israeli and Palestinian officials said following the talks.

The two leaders met for two hours at the prime minister's official residence in Jerusalem, a day after U.S. Secretary of State Condoleezza Rice urged Israel to do more to improve living conditions for Palestinians in the West Bank.

A Palestinian official said Monday the two sides have exchanged maps that suggest differences over the shape of a future Palestinian state are narrowing.

He said the Palestinians want all of the West Bank - which Israel captured in the 1967 Six-Day War - as part of their state, but are ready to give up nearly 2 percent of the territory in exchange for an equal amount of land from what is now Israel.

Maps presented by Israel several weeks ago sought to keep about 10 percent of the West Bank, the Palestinian official said. He said that despite the gaps, the maps indicated the sides are moving closer to a compromise on the issue of final borders.

After the talks, Olmert expressed readiness to make "tangible" changes in the West Bank, telling Abbas that he understands that their months of peace talks must be accompanied by action on the ground, an Israeli official said.

Abbas and Olmert also said following their meeting that they planned to work toward securing a peace settlement by the end of the year, as the United States has been urging throughout its mediation this year.

Concluding a a round of classic shuttle diplomacy on Monday, Rice affirmed that Israel and the Palestinians have the same clear goal to settle their worst differences this year.

"I think they know precisely what they are trying to do. They are trying to get to an agreement by the end of the year that is going to resolve the core issues," Rice told reporters as she left the region.

"I don't think there's any bad faith here - I don't," Rice added. "It's not undue caution to worry about the removal of obstacles that were put there for security reasons," she said.

"The puzzle," Rice said, "is to find ways to remove barriers to Palestinian movement that satisfy both sides."

She said the United States is checking back after roadblocks are lifted to see if the change helped, and recommended beginning the removal of barriers on an neighborhood-by-neighborhood basis.

"That is a very particular business," Rice said, "done at the level of one neighborhood or one business. That's really just more complicated work, and I think we're going to really start to do that."

Olmert's talks with Abbas came amid growing Palestinian dissatisfaction with the pace of negotiations. Abbas aides said the Palestinian leader was considering resigning if sufficient progress isn't made in the coming months.

A Palestinian official said prior to the meeting that Abbas planned pressed Olmert on West Bank settlements and military roadblocks during their meeting.

These two issues were given prominent mention by Rice during her latest diplomatic mission in the region

Abbas arrived at Olmert's residence just hours after Rice's departure for the latest in a series of sessions meant to push forward peace talks. With U.S. backing, the two men have set a year-end target for reaching a final peace deal to end 60 years of conflict, though the sides have recently expressed some doubts about meeting that goal.

On Sunday, Rice made unusually direct remarks about the consequences of Israeli construction and roadblocks in the West Bank, saying she continues to raise with the Israelis the importance of creating an atmosphere that is conducive to negotiations.

"That means doing nothing, certainly, that would suggest that there is any prejudicing of the final terms of a deal setting up a separate Palestinian state in the West Bank," Rice said.

Senior Palestinian negotiator Saeb Erekat said Monday's talks would include a broad look at how the negotiations are proceeding. He also said Abbas would urge the Israelis to curb settlement activity and lift many of the military checkpoints they have erected throughout the West Bank.

Abbas has sounded increasingly pessimistic in recent weeks. He has said that continued settlement construction on lands the Palestinians claim, and Israel's refusal to remove roadblocks and ease other travel restrictions, are undermining the negotiations.

Talks have made no obvious progress since getting under way at a U.S.-sponsored peace conference late last year. But during her visit, Rice insisted the date is still realistic.

Shortly after Rice's departure, a top Abbas aide sharply criticized the Bush administration. The aide, Nabil Abu Rudeineh, said the U.S. needs to step up its involvement and exert pressure on Israel to live up to its peace obligations, such as freezing Jewish settlements.

"That's why there should be American pressure on Israel, instead of continuous visits and statements," he said in a reference to Rice's frequent trips to the region. "Settlements are continuing, the siege is continuing, and Israelis aren't serious enough."

Abbas aides said the Palestinian president is giving the negotiations two or three months to produce progress and will consider resigning if he believes the talks have failed. They spoke on condition of anonymity because Abbas has not yet made a final decision.

Foreign Minister Tzipi Livni said at a press conference with Rice that Israel isn't trying to expand settlements as a way of seizing more land before an eventual withdrawal.

Livni pointed to Israel's 2005 withdrawal from the Gaza Strip as proof that Jewish settlements are not obstacles if the government decides it wants to pull out to achieve peace with the Palestinians. Israel dismantled 21 Jewish settlements in Gaza when it pulled out.

Abbas and members of his moderate government say Israel must make concrete moves to improve the Palestinian economy and show Palestinians why they should support the peace negotiations instead of radical groups like Hamas. But Israel says measures like roadblocks are vital parts of a security policy that has dramatically reduced militant attacks - and thus enabled peace talks to go ahead.

There was one suicide bombing last year and two so far this year. That's down from a record of 59 in 2002, the year Israel began building a separation barrier along the West Bank and multiplying its military checkpoints and roadblocks.