"Maybe, after 24 hours, there will be positive results," Palestinian legislator Hanan Ashrawi said Tuesday after meeting in Cairo with Amr Moussa, secretary-general of the Arab League.
Hamas and Islamic Jihad have said in principle they're ready for a cease-fire if Israel stops targeting their leaders and releases prisoners, reports CBS News Correspondent Robert Berger. They also want Israel to withdraw to positions held before the outbreak of fighting in September 2000.
Palestinian prime minister Mahmoud Abbas, who is making a final push to halt attacks on Israelis, met Tuesday with a U.S. envoy dispatched to the region to get a Mideast peace plan back on track.
The head of the U.S. monitoring team, John Wolf, held talks with Abbas ahead of the prime minister's meeting with Palestinian militias later in the day.
An Israeli official announced Tuesday that Secretary of State Colin Powell will arrive in Israel on Friday to meet with Israeli Prime Minister Ariel Sharon
"This visit is very important, I shall meet him. Of course, the prime minister will also meet him," Foreign Minister Silvan Shalom told Israel Radio.
Powell will travel to Israel a day after attending a meeting in Jordan with officials from other sponsors of the "road map" peace plan — the United States, United Nations, Russia and the European Union.
The plan envisions an end to 32 months of violence and the creation of a Palestinian state by 2005.
Israel says a cease-fire can only be a step toward dismantling the armed groups.
"They have to take immediate actions in order to put an end to terrorism, violence, and incitement here in the region," said Shalom.
Abbas has said he will not use force against the militias for fear of triggering civil war.
Israel has sent the head of its Shin Bet security service, Avi Dichter, to Washington to brief National Security Adviser Condoleezza Rice and other officials on the government's position regarding Hamas and a cease-fire.
Sharon's chief of staff, Dov Weisglass, met with Powell and Rice in Washington on Monday to prepare for a possible round of talks next weekend in the Middle East.
In a related development, Palestinian leader Yasser Arafat called the wife of imprisoned West Bank leader Marwan Barghouti early Tuesday and told her Israel would release Barghouti in the next two days. Barghouti is on trial for murder, charged with complicity in terror attacks that killed 26 Israelis.
Israeli political officials declined public comment on reports that Barghouti's release was being considered as part of the cease-fire package.
But Israeli Attorney General Elyakim Rubinstein wrote to Sharon that it would be "inconceivable" to release Barghouti, whom he described as a "first-rate architect of terrorism," before the trial has ended.
"Including Barghouti in some package deal with the Palestinians should not even be considered, the voice of our brothers' blood forbids it," Rubinstein wrote.
A source close to the talks said U.S. mediators would press Israel to end the targeted killings, and that if it succeeded, the militant groups would then agree to a truce.
The source, who spoke on condition of anonymity, said the Egyptians were asking for a written American guarantee of Israel's commitment on this issue, and on troop withdrawals and other steps implementing the road map.
Israeli officials insisted that they would continue targeting the militants and rejected the idea of a cease-fire that did not include a dismantling of the militias.
During more than 2½ years of violence, 2,400 people have been killed on the Palestinian side and 801 on the Israeli side.
The "road map" — authored by the United States, European Union, United Nations and Russia — begins with a halt to all violence and is to lead to a Palestinian state by 2005.
Sharon and Abbas both accepted the road map at the June 4 summit in Jordan with Bush, though Israel expressed many reservations.
Among other actions, the Palestinians are required to end violence against Israel, and Israel is to end settlement activity in the West Bank and Gaza — areas the Palestinians want for their state.