Mr. Bush also reacted skeptically to reports that three key militant groups had agreed to halt attacks on Israelis for three months. "I'll believe it when I see it," he said.
"The true test for Hamas and terrorist organizations is the complete dismantlement of their terrorist networks, their capacity to blow up the peace process," Mr. Bush said at a news conference with European Union leaders in Washington.
"It's one thing to make a verbal agreement," he said. "But in order for there to be peace in the Middle East, we must see organizations such as Hamas dismantled, and then we'll have peace, we'll have a chance for peace."
The president's remarks came hours after a senior official of Yasser Arafat's Fatah faction confirmed that three Palestinian groups, including Hamas and Islamic Jihad, had agreed to a cease-fire.
The official, Kadoura Fares, speaking on behalf of Fatah, said a formal statement about the cease-fire would be made later Wednesday. Fatah also signed the agreement.
Mr. Bush said he did not know details of the reported deal, but said he was dubious about it, "knowing the history of the terrorists."
CBS News Correspondent Robert Berger reports Israel has said it's ready to go along with a cease-fire to give the U.S.-backed peace "road map" a boost. But Israel says a cease-fire is just a first step, and all three terror groups must be dismantled.
White House spokesman Ari Fleischer said he could not confirm the deal. "Anything that reduces the level of violence is a step in the right direction," said Fleischer said. "But it's only a step."
Word of the agreement came as Israeli helicopters fired three missiles at two cars near the southern Gaza city of Khan Younis, killing two people.
The Israeli military said it targeted a Hamas cell that was about to fire mortar shells at an Israeli installation.
Hospital officials said a man and a 20-year-old woman were killed and 16 other people were injured in the attack. One of the cars belonged to Hamas activist Mohammed Masri, Palestinian security officials said.
Fares said that in recent days there have been intensive contacts between Fatah leader Marwan Barghouti, who is jailed in Israel, and Khaled Mashal of Hamas and Ramadan Shalah of Islamic Jihad, who are in Damascus.
The military wings of all three groups have carried out bombing and shooting attacks against Israelis during 33 months of fighting, killing hundreds.
"The Palestinian dialogue has resulted in a cease-fire agreement for a period of three months," Fares said.
A Palestinian source, who spoke on condition of anonymity, said a document outlining the truce terms was signed in Mashal, Shalah, and Barghouti.
In it, the militant groups agree to a moratorium on attacks for three months, the source said; in exchange they demand Israel end targeted killings of militants and military incursions, and call for the release of Palestinian prisoners held by Israel — but do not set any deadline or timeframe for this.
"We in the Fatah movement say this initiative should be followed by a comprehensive cease of aggression by the Israeli government against the Palestinain people," Fares said. "We consider this as a step to ending occupation and we salute the spirit of responsibility in the Hamas and Islamic Jihad."
Local Hamas leaders could not confirm the agreement. But Mohammed al-Hindi, the top Islamic Jihad leader in the Gaza Strip, said Hamas agreed to a three-month truce and was trying to arrange a joint declaration with his group.