"If it's possible to make him happy and make me happy, then I can't see a reason not to do it, and hope that it will happen very soon," Olmert said during a press conference in Jerusalem with Norwegian Prime Minister Jens Stoltenberg.
In his first public comments on the crisis in Gaza, Olmert he hopes a cease-fire between the warring Palestinian factions would stick.
"We are not happy about the developments in the Palestinian Authority," Olmert told the news conference.
"Mutual violence between Fatah and Hamas is not something we are happy to see. We definitely would be happy to see a cease-fire."
A meeting between Olmert and Abbas is expected to take place in the coming days, Palestinian sources said on Tuesday, although in Israel a date has not been confirmed.
"As far as we are concerned we can meet tomorrow," sources in the Prime Minister's office said Tuesday. "Efforts are being made to coordinate a meeting but no date has been set," they added.
Also Tuesday, Olmert made a lightning visit to Jordan for a meeting with King Abdullah II.
A Palestinian source close to Abbas said that the first official meeting with Olmert is likely to take place next week.
Senior PLO negotiator Saeb Erekat confirmed Tuesday that efforts were being made to set up a meeting between the two leaders.
"Preparations are being made, and the moment these are completed, the meeting will take place," Erekat said.
The source told Haaretz that possible dates are December 24 or 25, and, at the latest, January 1 or 2.
According to the source, the two leaders would like to hold the meeting before U.S. Secretary of State Condoleezza Rice arrives to the region in early January.
The Palestinians are eager to see Israel making a number of gestures that would bolster Abbas in the Palestinian Authority, including the release of prisoners and the easing of travel restrictions, the source said.
The same source said this would be an opportunity for Israel to also release some of the funds it has frozen, collected from taxes and customs on behalf of the Palestinian Authority.
The visit to Ramallah of Olmert's senior policy adviser, Shalom Turjeman and Olmert's chief of staff Yoram Turbowicz last week, the Palestinian source said, was interpreted among Abbas' aides as a sign of goodwill that will bring about closer ties between the staff of the two leaders.
Releasing Palestinian prisoners prior to a deal for the freeing of abducted Israel Defense Forces soldier Gilad Shalit will prove that Israel is willing to initiate action, even when it does not come under military pressure, the Palestinian source said.
Olmert meeting with the Jordanian king on Tuesday revolved around the crisis in the Palestinian Authority and ways to bolster Abbas.
Following the meeting, a Jordanian source said Abdullah would invite Abbas and Palestinian Prime Minister Ismail Haniyeh to a meeting in Amman to help in mediating between Fatah and Hamas.
This is a new development in light of the fact that Abdullah has shunned Hamas because of its role in terrorism in the Hashemite kingdom.
Abdullah stressed during his meeting with Olmert that Israel and the Palestinian Authority must find a way to hold direct negotiations.
During the two-hour meeting, Abdullah warned Olmert against losing time in a peace process that is at a standstill because this would lead to violence "in which all sides will pay a price."
The Jordanian king asked Olmert to consider seriously the Arab League's initiative for peace - originally made in Beirut in 2002 and since reiterated on a number of occasions.
The two leaders also discussed strategic and economic issues of mutual interest, including the Peace Valley project proposed by Vice Premier Shimon Peres, a political source in Jerusalem said.
A very small portion of the meeting was dedicated to Iran.
Olmert's visit to Amman was prepared a month ago but was kept secret until its completion, in compliance with a request by Jordan.
Abdullah and Olmert met privately for about an hour and were then joined by aides for a broader exchange of views.
Taking part on the Israeli side were Turbowicz, Turjeman, and Major General Gadi Shamni, military secretary of the Prime Minister.
During the meeting the Jordanians raised the passage of the Badr Brigade, a Palestinian unit in the Jordanian army, from Jordan to the Gaza Strip, which is one of the ways of bolstering Abbas in the Hamas stronghold.