WASHINGTON — In separate meetings with Middle East leaders yesterday, President Bush applauded Lebanon’s efforts to forge a national reconciliation and told President Abbas of the Palestinian Authority that America has not given up hope on an agreement to create a Palestinian Arab state.

“I appreciate your determination and your desire to have a Palestinian state,” Mr. Bush told Mr. Abbas in front of reporters before a White House meeting. “I share that desire with you. It’s not easy.”

Mr. Bush said the administration will continue to work with Palestinian authorities on security matters and on helping to coordinate international economic assistance.

“As you know, I’ve got four more months left in office and I’m hopeful that the vision that you and I have worked on can come to pass,” he added.

Mr. Abbas, seated beside Mr. Bush, told the president that he was thankful for American support.

“Hope remains,” Mr. Abbas said. “We cannot live without hope.”

According to a Palestinian Arab negotiator, Saeb Erekat, who attended the meeting, Mr. Abbas said Palestinians are seeking “a comprehensive agreement on all the issues, without any exception. Either there will be an agreement on all the issues or there will be no agreement.”

Middle East peace talks were relaunched at an American-hosted summit last November, and with prodding from America, Israel and the Palestinian Arabs set a year-end target for reaching a final peace accord that would end six decades of hostilities.

Despite months of negotiations, there have been no apparent breakthroughs, and the sides remain at odds over key issues like the final borders between Israel and a future Palestinian Arab state, the competing claims to Jerusalem and the fate of millions of Palestinian refugees.

Negotiations have been stalled by the resignation of Prime Minister Olmert, who stepped down amid a string of corruption allegations. Tzipi Livni, Israel’s prime minister-designate, has signaled that she will keep peace negotiations going.

In an earlier meeting yesterday, Mr. Bush lauded efforts by Lebanon’s new president to promote reconciliation in a country America considers key to combatting extremism in the Middle East.

In remarks at the outset of the Oval Office meeting with President Suleiman, Mr. Bush said he has watched carefully the public statements that Mr. Suleiman has made since taking office in May.

“Your statements impressed me and we’re most impressed by the national dialogue that you’re holding in an attempt to seek reconciliation,” Mr. Bush said. “The United States is proud to stand by your side. Our mission is your mission: a country that is strong and capable, a country where people can make a peace.”

Mr. Suleiman, seen as relatively friendly with Syria, was installed as president in a compromise after Hezbollah blocked pro-Western factions from electing a politician who took a harder-line stance against Syria. Mr. Suleiman’s talks with Mr. Bush yesterday also were expected to cover the expansion of the Lebanese army and peace talks between Syria and Israel.

Under Lebanon’s sectarian power-sharing system, the post of prime minister goes to a Sunni Muslim. The majority is headed by Sunnis while the opposition is led by Shiites. Clashes last May between Hezbollah’s Shiite supporters and pro-government Sunni loyalists in Beirut and other areas left 81 people dead and more than 200 wounded.

Sitting beside Mr. Bush in the Oval Office, Mr. Suleiman said his country shares many American values, including the promotion of liberty and the fight against terrorism. And he thanked Mr. Bush for his administration’s support of the Lebanese government, particularly efforts to bolster the Lebanese army.