Israel has said that for now it would accept a cease-fire from the militants, though it wants Palestinian officials to act to disarm and disband the groups as soon as possible.
The security issue has been a main sticking point in starting the U.S.-backed road map to peace, a three-stage plan aimed at creating a Palestinian state in 2005.
Following similar meetings with the Israelis earlier, U.S. officials met Palestinian Prime Minister Mahmoud Abbas to haggle over the road map's first step: declarations by each side recognizing the other's right to statehood and security.
U.S. officials want the declarations ready when Mr. Bush meets Abbas and Israeli Prime Minister Ariel Sharon in a summit Wednesday in the Jordanian port city of Aqaba.
In talks between Abbas and U.S. Assistant Secretary of State William Burns on Saturday, the Americans accepted Abbas' position that there must first be a cease-fire before militant groups can be dismantled, Palestinian Foreign Minister Nabil Shaath said.
"This is an important goal for us," Shaath told reporters. Neither Burns nor Abbas made a statement. The U.S. Embassy declined to comment on Shaath's statement.
Abbas has said he preferred persuasion to stop suicide bombings and other anti-Israeli attacks, and that within days he could have a cease-fire agreement with Hamas, the main group carrying out attacks.
The Israelis have demanded Abbas wage a crackdown. A Sharon aide said Friday that the Israelis would accept a cease-fire first, but that it must be the first stage of action.
Meanwhile, the militant group Islamic Jihad distributed fliers Saturday saying it has "no intention of attacking the American people and do not consider the American people our enemy" a response to a warning the U.S. Embassy posted on its Web site Friday saying it had received "credible reports" of plans to kidnap U.S. citizens in the Gaza Strip.
Hamas issued a similar statement Friday.
The warning was still posted on the embassy site Saturday.
Hamas and Islamic Jihad have claimed responsibility for scores of attacks in Israel that have killed more than 350 people in the past 32 months. Though Americans have been killed over the years in the Mideast conflict, they have usually died in attacks that targeted Israelis, not Americans.
Two Palestinian militants died Saturday. The first, a 21-year-old Hamas activist identified as Mohammad Shalash, was killed by Israeli troops south of the West Bank city of Jenin, Palestinian witnesses said.
The army said troops fired at two militants who were planting a large explosive device along a road used by Israeli troops, hitting one. The other was captured after a short pursuit. The army detonated the 65-pound device later in a controlled explosion.
Hisham Tafesh, 22, also identified as a militant, died Saturday in a Gaza Strip hospital, Palestinian hospital officials said. The Israeli army said Tafesh had tried to plant a bomb Thursday near the Jewish settlement of Kfar Darom in Gaza when it exploded. His alleged accomplice, Mohammad Abu Sbeitan, was killed instantly.
The declarations by the Israelis and Palestinians recognizing the rights of the other to security and statehood are supposed to be the first step of the U.S.-backed road map peace plan, which begins with a halt to the violence. In its first stage, it also calls for a freeze in Jewish settlement construction.
Shaath said Saturday the Americans made a commitment to "move ahead with the implementation of the road map with all its details."
Burns and Elliott Abrams, who heads the Middle East desk at the National Security Council, met separately Friday with Palestinian security chief Mohammed Dahlan and Israeli Foreign Minister Silvan Shalom. U.S. officials have told both sides the United States intends to set up American-led groups to closely monitor implementation of the road map.
The PLO's legislative committee authorized Abbas and Palestinian leader Yasser Arafat to choose Palestinian delegates for the summit, the official Palestinian news agency said Saturday. Israel and the United States have been trying to sideline Arafat, charging that he is involved in Palestinian terrorism. Under the law that created Abbas' post, however, the PLO executive has the final say on peace talks.
Israeli media reported Israel might start easing restrictions as soon as Saturday night on Palestinians in the West Bank and Gaza in accordance with promises Sharon made to Abbas at a Thursday meeting.
The expected measures include partially lifting a closure on the West Bank, allowing some Palestinians into Israel to work and opening fishing areas off the Gaza coast. Israel also has promised to release about 100 of 1,000 Palestinians held in military detention centers without trial or charges. It was not known when the prisoners would be released.