"I want to take this opportunity and say that I am sorry for the grave accidents in which innocent Palestinians were killed. This is not Israel's policy, but malfunctions," he said.
Olmert made the comments in response to questions by Nobel Prize Laureate Elie Wiesel at the Petra summit.
Olmert was hosted by Jordanian King Abdullah. The Israeli prime minister met with Palestinian President Mahmoud Abbas.
Olmert and Elie Wiesel at Petra summit (Photo: AFP)
"The situation with the Palestinians necessitates serious concessions. We need to change the situation with them, we need to make a painful compromise," Olmert said.
Olmert told reporters of his intention to meet Abbas within weeks: "We decided to meet within weeks. We will talk. It's not me, it is the Quartet and the international community who set the conditions for talks: recognizing Israel, rejecting terror, and respecting agreements signed with the Palestinian Authority since 1993. If the conditions are fulfilled, we can hold serious negotiations."
'Palestinian books full of hatred and incitement'
The breakfast in the ancient Jordanian town of Petra sponsored by Jordan's King Abdullah ll, appeared to produce the desired effect: Promises on both sides of a more substantive meeting to come. It also brought a rare apology from Olmert for the deaths of 14 Palestinian civilians in Israeli air strikes in recent days.
"It is against our policy and I am very, very sorry," he said.
"I think that Abu Mazen is a genuine person and he comes here with good intentions," Olmert said after meeting Abbas, using the Palestinian leader's nickname.
"But to the best of my knowledge, he is not the prime minister of the Palestinian Authority," Olmert said.
He also criticized the Palestinian education system: "Palestinian books are shocking. They are full of hatred and incitement and children are exposed to horrible slogans and caricatures."
Meanwhile Thursday, dozens of children took to the streets of Gaza city to protest deadly air strikes carried out by the army. Some protesters gathered outside the United Nations building in the city, demanding international intervention.
AP contributed to the report