Palestinians say a meeting between President Yasser Arafat and Israeli Foreign Minister Shimon Peres to discuss a shaky cease-fire could come as early as Sunday.
The United States and other countries have been urging Mr. Arafat and Mr. Peres to meet to strengthen a truce agreed to earlier this week.
Such a meeting between the two leaders has been postponed a number of times because of continuing violence in the Israeli-Palestinian conflict, which has lasted nearly one year.
Mr. Arafat says he hopes to meet with Mr. Peres on Sunday, if the Israelis do not change their mind.
Israeli Prime Minister Ariel Sharon says there must be 48 hours of complete calm before truce talks can take place.
Mr. Peres said on Saturday that, while the situation has improved, Israel is still not satisfied because of continuing clashes.
The current cease-fire has sharply reduced the bloodshed, although sporadic acts of violence are continuing.
The Israeli army says Palestinians fired mortar shells in the Gaza Strip, grenades were hurled at an army post in Gaza, and there was an exchange of gunfire near the West Bank city of Bethlehem.
Hospital officials said on Saturday a Palestinian security officer died from wounds received in clashes earlier this week with Israeli soldiers.
Manuel Hassassian, a professor of political science and Middle East studies at Bethlehem University, says it is very difficult for Mr. Arafat to completely stop the violence. "I have a strong conviction that President Arafat will control the situation now, regardless that there have been incidents here and there after the cease-fire call," he says. "This is very normal, because it is very hard to control the emotions of people and the emotions of those who are involved in defying occupation. So Arafat does not have a remote control to stop everyone instantly."
Calm in the region is seen as crucial to America's efforts to recruit Arab and Islamic countries into an anti-terror coalition, after the attacks on New York and Washington.
Israeli and Palestinian officials say the Bush administration, which had been hesitant about interfering in the Middle East conflict, has become more involved since the attacks on America.
Western diplomats say the administration has been working closely with the European Union and the United Nations, in an effort to revive the deadlocked peace process.
EU leaders are sending a ministerial mission to the Middle East next week, which is expected to focus on the diplomatic process.