Story Highlights• NEW: Condoleezza Rice meets with Israeli officials, praises cease-fire progress
• Earlier, Rice met with Palestinian Authority President Mahmoud Abbas
• Secretary of state says U.S. backs "viable and contiguous" Palestinian state
• Abbas says efforts on Palestinian unity government have reached a "deadlock"
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JERUSALEM (CNN) -- U.S. Secretary of State Condoleezza Rice met with Israeli and Palestinian leaders Thursday in an effort to capitalize on recent moves to achieve peace in the Mideast, including a cease-fire in Gaza.
"Indeed, it has been a week of progress, a week that we hope can be consolidated," Rice said at a Jerusalem news conference with Israeli Foreign Minister Tzipi Livni.
Israel agreed to withdraw troops from Gaza after a cease-fire with Palestinian factions over the weekend. The cease-fire has held despite Palestinian militants firing some rockets into Israel. (Full story)
"The cease-fire now needs to be consolidated by action to make certain that it is enforced," Rice said. (Watch shift in U.S. diplomacy in Mideast )
"I also appreciate the statements of restraint that the Israeli government has issued concerning the cease-fire, because it is of course quite fragile, but we would like to see it consolidated and then extended."
Rice spoke to reporters after her meetings with Livni and Israeli Prime Minister Ehud Olmert.
Earlier Thursday, she met with Palestinian Authority President Mahmoud Abbas in the West Bank town of Jericho. At a news conference with Abbas, Rice praised Olmert for offering concessions to the Palestinians, including a prisoner exchange.
She called a speech that Olmert gave Monday "a very positive development" and "an effort to reach out to a Palestinian partner." (Full story)
Olmert's offer to free Palestinian prisoners in exchange for an Israeli soldier whom militants captured more than five months ago is a turnaround from an earlier demand that the abductors free the soldier without conditions.
Rice expressed U.S. commitment to a "viable and contiguous" Palestinian state and voiced concern for the deteriorating humanitarian conditions for Palestinians, especially in Gaza.
"We want to do everything that we can to ease movement and access" for the Palestinian people, she said. "The daily difficulties, the daily humiliations that are associated with life for the Palestinian people simply must be eased. ... I will work with you, Mr. President, and the Israelis to do precisely that."
Abbas said efforts to form a Palestinian unity government -- necessary to resume the flow of international aid halted after Hamas took power earlier this year -- have reached a "deadlock."
"This is very painful to us -- we know how badly our people suffer because of the difficulties they have faced," Abbas said. "They have been denied resources, but unfortunately we failed. We did not succeed."
Though continuing to deal with Abbas, the Bush administration has cut ties to the Hamas-led Palestinian government until it agrees to renounce calls for the destruction of Israel.
The United States, Israel and the European Union consider Hamas a terrorist organization, but it won control of the Palestinian Authority in parliamentary elections in January.
Rice: U.S. hopes cease-fire will extend to West Bank
Rice praised Abbas for his role in reaching a cease-fire with the Israelis in Gaza last weekend and expressed hope that it will become "comprehensive," to include the West Bank.
Palestinian leaders dispatched 13,000 troops to the Gaza-Israel border to enforce the agreement after some militants' rocket attacks into Israel, Abbas' office said. (Watch threats to peace as cease-fire takes hold )
Rice's meetings in Jericho and Jerusalem come between sessions of a foreign ministers' conference she is attending in neighboring Jordan.
The conference host, Jordan's King Abdullah II, said Sunday the Israeli-Palestinian conflict is the root of other troubles in the Middle East, including the war in Iraq and crisis in Lebanon. (Full story)
British Prime Minister Tony Blair also has called for a renewed focus on settling the decades-old conflict as part of a broader solution to the region's problems.
Israeli Foreign Minister Tzipi Livni, left, greets U.S. Secretary of State Condoleezza Rice on Thursday in Jerusalem.
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