Mr Olmert expressed his “deep regret and sorrow” over the deaths of innocent civilians, and said he would “put everything on the line” for peace.
The meeting follows a surge in tensions, with 14 Palestinian civilians, including five children, killed in Israeli air strikes on Gaza in nine days.
“It is against our policy and I am very, very sorry,” Mr Olmert said after a breakfast meeting with Mr Abbas in the ancient Jordanian town of Petra, hosted by Jordan’s King Abdullah II.
However he later said Israel will continue striking at militants. Both sides insisted it was not a formal encounter, but they want to resume talks.
Mr Olmert cautioned against high hopes, and suggested that peace talks could only go ahead if the Palestinian Hamas government recognises Israel.
“I pray the Palestinians will have the courage to get rid of extremists and fundamentalists and put in place the right people to move on recognition,” he said.
But Mr Olmert also set down conditions to ensure the success of future meetings with the Palestinians.
“There should be fulfilment on three, non-negotiable conditions: total disarmament of terrorist organisations, full implementation of agreements and formal recognition of Israel,” he said.
Mr Abbas, a moderate elected separately last year, is in an intense power struggle with Hamas, and is trying to persuade Israel to bypass the militant group and negotiate directly with him.
Palestinian Prime Minister Ismail Haniyeh belongs to the militant Islamic Hamas, which rejects Israel’s right to exist, has sent dozens of suicide bombers into Israel and refuses to renounce violence.
Mr Abbas has been seeking to persuade Hamas to accept a proposal that implicitly recognises Israel as a way to restart peace talks and end a crippling world aid boycott.
If Hamas continues to reject the proposal, the president plans to bring the plan to Palestinian voters in a July 26 referendum.
The meeting took place on the sidelines of a two-day gathering of Nobel Prize winners, which also included the Dalai Lama, a deputy Thai prime minister and Elie Weisel, a Holocaust survivor and the 1986 Nobel Peace Prize winner.
The Jordanians saw the breakfast meeting as an effort to warm relations between Israel and the Palestinians, and the encounter seemed to produce the desired effect. The ice was broken and both sides promised a more substantive meeting in coming weeks.
The two men shook hands, embraced and kissed each other on the cheek. Asked about his handshake with Mr Olmert, Mr Abbas said: “It was very warm, very warm.”