(Adds details) SHARM EL-SHEIKH, Egypt, June 25 (Reuters) - Israeli Prime Minister Ehud Olmert said on Monday he intended to free 250 Palestinian prisoners from Israeli jails in a gesture to President Mahmoud Abbas, leader of the Fatah faction. At a news conference in Egypt with Palestinian, Egyptian and Jordanian leaders, Olmert said a new opportunity had been created to promote the Middle East peace process and that he would not let that opportunity pass. Abbas sacked a Palestinian unity government led by Hamas and formed an emergency administration of his own in the occupied West Bank after Hamas Islamists, who are shunned by Israel, seized control of the Gaza Strip just over a week ago. "The new government in the Palestinian Authority recognises Israel's right to exist ... and opposes terror and violence as a means of achieving its goals," Olmert said, adding that it was a government that Israel recognised. "We will act together," Olmert said. In addition to promising to free the 250 prisoners in Abbas's secular Fatah faction, Olmert said he would ease travel restrictions in the West Bank, but he offered no details. Aides said he was unlikely to start removing checkpoints and roadblocks before Abbas took more steps to rein in militants. "I'm optimistic that, especially in these turbulent days ... an opportunity has been created to seriously move forward with the regional peace process. I don't plan to let this opportunity slip away," Olmert said. He said the 250 prisoners to be freed were members of Fatah "who do not have blood on their hands" and who had given a "commitment not to involve themselves again in terror". Israel holds about 10,000 Palestinians in its jails. Olmert said both he and Abbas were sure to be criticised at home for the steps they have agreed to take. "This is the time to show leadership, to lead public opinion and not be afraid of it," Olmert said.