Israeli Prime Minister Ehud Olmert and Palestinian Authority President Mahmoud Abbas have met for the first time in a year, at an informal breakfast.
Mr Abbas (left) and Mr Olmert (far right) did not hold one-to-one talks
The pair attended the event in the Petra, Jordan, hosted by King Abdullah.
Both sides insisted it was not a formal encounter, but said they were planning for another meeting soon.
The two men have said they want to resume peace talks, but Mr Olmert says the Hamas-led Palestinian government must recognise Israel and stop attacks.
Mr Olmert and Mr Abbas shook hands and embraced on meeting in Petra, but it was not a one-to-one event - others joining them on the sidelines of a Nobel conference included Nobel Prize winner Elie Wiesel and the Thai deputy prime minister.
The Israelis were not even calling the breakfast a meeting, although Mr Olmert travelled to Jordan especially for the occasion.
And after the event, Mr Olmert said he would meet the Palestinian president again - although he cautioned serious negotiations were unlikely until the Hamas-led Palestinian government recognised Israel, the Associated Press reported.
The Petra meeting comes at a time of rising violence between Israel and the Palestinians.
There are also deep divisions between Palestinian factions, with senior officials from Hamas and Fatah locked in talks to try to resolve their differences.
The two leaders shook hands on meeting for the first time in year
Officials have said the factions are close to agreement on an initiative that would implicitly recognise Israel.
Hamas has so far refused to recognise Israel's right to exist - in contrast to Fatah's position.
Mr Abbas, who leads the Fatah movement, has threatened to hold a referendum next month on the plan unless Hamas accepts it.
The plan sets out formal Palestinian claims to an independent state on land occupied by Israel in 1967, and implicitly adopts a two-state solution.
Israel's Deputy Prime Minister Shimon Peres, at Thursday's meeting in Petra, said that to negotiate with the Palestinians "completely and seriously, we have to see what happens on the Palestinian side, and the Palestinian side is, until now, inconclusive," the Associated Press reported.
But he described the contact between Mr Olmert and Mr Abbas as "fruitful and positive", the agency said.
As well as recognising Israel and stopping attacks, Israel is demanding that Hamas accept past peace agreements between Israel and the Palestinians.
He has said that if attempts to negotiate fail, he will push ahead unilaterally with plans to re-draw Israel's border with the Palestinians.