Olmert's visit came in response to an invitation by Abdullah, who is eager to see Israel resume peace negotiations with the Palestinians, a senior palace official said.
In Jerusalem, Olmert's office confirmed the meeting, saying the leaders discussed the Palestinian crisis and larger regional issues.
The U.S.-allied monarch has said a return to Arab-Israeli negotiations is vital to curb rising extremism in the Middle East, fueled by the conflict in Iraq. Abdullah has called on Washington to do more on reviving the peace process, which is stalled amid the Palestinian crisis.
The palace official, who spoke to The Associated Press on condition of anonymity because of the sensitivity of Olmert's visit, said the two leaders met for two hours and the Israeli then returned home.
In the talks, Abdullah urged Olmert to "engage in negotiations with the Palestinians so that an appropriate framework could be found to relaunch the peace process," a palace statement said.
It said the king told Olmert that "in order to foster confidence in the peace process, it was critical to show people on both sides of the conflict that there are credible partners for peace."
Abdullah also voiced his vision for peace — "a two-state solution" with separate Israeli and Palestinian nations living side by side.
"This is the only logical solution and the only way to fulfill the Palestinians' aspiration to establish a sovereign, viable state and Israelis' need to achieve security and stability," the statement quoted him as saying.
The king, whose nation signed a peace treaty with Israel in 1994, had hosted Olmert and Palestinian President Mahmoud Abbas in June in a failed effort to get both leaders to open direct negotiations.
The peace process has been stagnant since 2000 and efforts to restart talks have failed in the face of the factional violence wracking the Palestinian territories.
The palace statement said Abdullah briefed Abbas on his talks with Olmert in a telephone call, but provided no details of the conversation.
The palace also said Abdullah would invite the leaders of Hamas and Fatah to talks on ending their conflict.
"Jordan is willing to do all it can to help the Palestinians overcome their differences and to bolster Palestinian unity," the statement said. "All options are open, including a call for a meeting in Amman between Palestinian leader (Abbas, of Fatah) and Palestinian Prime Minister Ismail Haniyeh (of Hamas)."
The discussions would focus on "ways to end the political crisis between their Hamas and Fatah movements," the statement said.
Hamas said it had not yet received the invitation.
"If we receive a formal invitation, it will be studied and addressed in harmony with national interest," said the group's spokesman, Fawzi Barhoum.
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Posted 12/19/2006 9:08 AM ET