Rice's first stop was in the West Bank city of Jericho, where she met with Palestinian Prime Minister Mahmoud Abbas at a plush hotel. Before the meeting, Abbas said he would press her for guarantees on the release of Palestinian prisoners held by Israel.
Rice's visit also includes a meeting with Israeli Prime Minister Ariel Sharon on Sunday, when militant groups are planning a formal announcement that they are halting attacks against Israelis for three months. However, some militants suggested the announcement might be delayed a day.
Together with a preliminary agreement by Israel to pull out troops from the Gaza Strip and West Bank town of Bethlehem, a truce could be a significant turning point that provides a major boost to the "road map" peace plan launched by President Bush at a June 4 Mideast Summit.
Violence has plagued attempts to implement the road map, a blueprint to end 33 months of fighting and establish a Palestinian state by 2005.
On Saturday, two explosive devices detonated, damaging at least one vehicle in a convoy of U.S. diplomatic cars traveling in Gaza, Israel's military said. No injuries were reported and U.S. embassy officials refused to comment on the incident.
The Syrian-based leaders of the two main Islamic groups, Islamic Jihad and the larger Hamas group, agreed to a truce earlier in the week, according to a Palestinian legislator involved in the negotiations. But Gaza-based militants initially denied there was a deal, and then said details remained to be worked out.
"We have accepted a conditional cease-fire for three months," Mohammed al-Hindi, an Islamic Jihad leader in Gaza, told The Associated Press on Saturday, in the first on-the-record confirmation of the truce from a militant leader.
A formal announcement was expected Sunday, but Al-Hindi said it could be put off until Monday, if necessary.
Hamas leaders have also said they agree to a truce, but will only formally declare their acceptance in a joint document still being finalized.
The truce, first reported by AP on Wednesday, applies to the West Bank and Gaza, as well as Israel, fulfilling a key Israeli demand. Militants groups often distinguish between attacks on Israel proper and strikes against Israelis living or working on occupied territories seized by Israel in the 1967 Six Day War.
Intensive meetings continued Saturday between Islamic Jihad, Hamas and Palestinian leader Yasser Arafat's Fatah faction to work out the final wording of the truce announcement.
There were also efforts to bring 10 smaller factions on board. Some smaller bands say they were not consulted on the deal. Others may lack the internal controls to prevent new attacks anyway.
Israel and the United States have given the emerging truce a lukewarm response. Both want the Palestinians to disarm Hamas and other violent groups, but Abbas has said doing so would risk a civil war. Abbas lacks broad popular support and his security services have been decimated in fighting the Israelis.
The White House welcomed a preliminary agreement Friday to turn over security responsibility in Gaza and Bethlehem to the Palestinian Authority, calling it a "first significant joint step toward implementation of commitments" Israeli and Palestinian leaders made at the June 4 summit with Mr. Bush.
The road map requires that Israeli forces gradually withdraw to positions held before the outbreak of fighting in September 2000.
Israel was "cautiously optimistic" about the pullback arrangements, Foreign Ministry Spokesman Yonatan Peled said Saturday, but expected the Palestinian Authority to "keep a lid on terrorist activity emanating from the Gaza Strip."
The deal, reached in talks between Palestinian security chief Mohammed Dahlan and Israel's Maj. Gen. Amos Gilad, came with a pledge by Israel to halt targeted killings of wanted Palestinians — one of the militants' key demands for continuing with a truce.
Palestinians in turn agreed to act against what Israel calls "ticking bombs" — assailants on their way to attack Israelis. But Peled said Israel reserved the right go after assailants themselves if Palestinians failed to do so.
Israel says it will give the Palestinians one chance, reports CBS News Correspondent Kimberly Dozier. After its troops withdraw, Israel will pass on any intelligence it receives of an imminent attack.
Arafat's Fatah approved the deal at its weekly Saturday meeting. Details of how to implement it were to be worked out at meetings Sunday in Gaza and Bethlehem.
The progress in negotiations was accompanied by mounting pressure by Palestinians for guarantees regarding the release of prisoners. Some have already been freed from Israeli jails.
Abbas told a crowd of angry demonstrators that he would press for more releases. Israel said future releases were possible, if progress was made toward curbing violence.