The king, considered a moderate among Arab leaders, came to Washington with the purpose of urging Mr. Bush and his administration to take an aggressive role in reopening the shelved peace negotiations.
The president, during a picture-taking session with the king in the Oval Office, said, "Our country is very interested in working with all parties."
In a thinly veiled message to Arab leaders, most of whom back Yasser Arafat and the Palestinians in their uprising against Israel, Mr. Bush said it is important that all parties use their influence to stop the violence.
For his part, the king said of the president: "I believe we're both committed to finding peace and stability in our part of the world."
On an issue vital to the king and his hard-pressed economy, which used to depend heavily on trade with now-sanctioned Iraq, Mr. Bush said his administration would do what it can with Congress to try to get a free-trade agreement for Jordan on track.
U.S. Trade Representative Robert Zoellick sat in on the leaders' private meeting, as did Vice President Dick Cheney, Secretary of State Colin Powell and national security adviser Condoleezza Rice.
Before the meeting, Mr. Bush and the king shared lunch. The president described the session as productive and meant "to lay the foundation for peace in the Middle East."
Abdullah has spent a week lobbying America's power elite for support, pressing his idea that the United States is essential to bringing peace to the Middle East.
"The United States has played a tremendously positive and important role in the peace process since its launch in Madrid," Spain, in 1991, Abdullah said shortly before his arrival in Washington. "This role remains essential, and we will be discussing how we can work together, and with regional parties to restore calm and get the peace process back on track."
But Abdullah stressed in a television interview that "the emphasis no is on the Israelis and Palestinians" to prove they are trying to end six months of violence.
Abdullah called the perception in the Mideast that the United States has abandoned the peace process "wrong," saying the Bush administration is waiting for stronger signs of cooperation from Israel and the Palestinians before plunging in.
"The American administration feels, quite rightly I believe, that both sides need to sit down together and show that they're willing to take the risk to move forward, at which point the Americans would be there to help them," Abdullah said Monday night on "The NewsHour With Jim Lehrer" on PBS.
On Monday, the State Department announced that Israeli and Palestinian leaders had agreed "in principle" to hold additional security meetings on how to quell violence in the region.
Abdullah said such meetings were a "small step in the right direction."
The Jordanian leader discussed how to deal with violence in the turbulent region during a meeting last week with Powell. The two also talked over economic issues affecting Jordan, including free trade with the United States.
Israeli Prime Minister Ariel Sharon and Palestinian leader Yasser Arafat told Powell during separate telephone conversations that each was willing to hold further meetings similar to an inconclusive one last week in Israel.
Powell spoke with the leaders Sunday "to encourage the two sides to continue their bilateral security discussions," State Department spokesman Richard Boucher said.
"We'd say both parties were positive in their assessment of last week's meeting," Boucher said. "They've agreed, in principle, to continuing those discussions and we will continue to work with the parties to try to see if we can help them do that."
By Eun-Kyung Kim
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