The militant groups announced three-month truces and Fatah's cease-fire is for six months.
At sundown Sunday, Israeli troops and tanks began pulling out of northern Gaza, in keeping with an agreement to hand responsibility for security in Gaza over to the Palestinians.
An Israeli pullout is a condition of the U.S-backed "road map" to peace and a Palestinian state by 2005.
"Anything that curtails the cycle of violence in the Middle East is welcome news to the White House," reports CBS News Correspondent Mark Knoller.
A spokeswoman called the truce a step in the right direction, but in the White House view, a temporary suspension of attacks is not enough. President Bush is demanding that groups such as Hamas be permanently dismantled.
"Under the road map, parties have an obligation to dismantle terrorist infrastructure," said White House spokeswoman Ashley Snee. "There is still more work to be done."
The truce was first announced by the two militant groups. The timing came as a surprise, since Palestinian officials had said it would be delayed at least until Monday because of political infighting in Arafat's Fatah movement, a partner in the three-way deal.
Hamas and Islamic Jihad apparently did not want to wait for Fatah to resolve its internal agreements.
Abdel Aziz Rantisi, a Hamas leader, read the truce announcement in a phone call to The Associated Press.
"The two movements (Hamas and Islamic Jihad) decided to suspend military operations against the Zionist enemy for three months, starting today," Rantisi said.
Islamic Jihad leader Mohammed al-Hindi confirmed that the truce took effect on Sunday.
"This is a joint declaration between Islamic Jihad and Hamas and I think our brothers in Fatah are going to declare their position soon," al-Hindi told the AP.
Hours later, Fatah issued a statement saying it would halt all military operations in accordance with an Egyptian initiative calling for a six-month truce.
Israeli officials said they fear the truce will be used by militants to regroup for more attacks against Israel. Israel wants the Palestinian Authority to dismantle militant groups like Hamas and Islamic Jihad, as required by the road map plan.
"We are not holding our breath," Foreign Ministry spokesman Gideon Meir said. "We here in Israel fully support the road map, and we want it to be implemented chapter and verse."
Rantisi reiterated a list of demands — although not preconditions — for the suspension of attacks. Hamas and Islamic Jihad have said they want Israel to halt all military strikes, including targeted killings of wanted militants such as a recent attack on Rantisi.
The groups also want a release of Palestinian prisoners.
"We consider ourselves free from this initiative if the Israeli enemy does not implement all the conditions," Rantisi said.
Before Fatah declared its cease-fire, its Central Committee met to try to defuse its crisis over the truce. Key members of the group — led by Arafat and Palestinian Prime Minister Mahmoud Abbas were upset at being kept out of negotiations.
Talks with Hamas and Islamic Jihad, the main political rivals of Fatah, were largely handled by Marwan Barghouti, a Fatah leader jailed by Israel.
Fatah members angered by the back-channel talks had insisted Sunday that the introduction to the document be changed and that the U.S.-backed "road map" be mentioned, according to officials close to the dispute. Such an addition would be unacceptable to Hamas and Islamic Jihad, which have rejected the plan.
Over the weekend, the three main groups held talks with 10 smaller factions on joining the truce.
In one snag, the Popular Front for the Liberation of Palestine, a radical PLO faction, told Palestinian officials Sunday that while it would not join a declaration, it would not violate a truce.
In Jerusalem, meanwhile, U.S. National Security Adviser Condoleezza Rice held talks Sunday with Israeli Prime Minister Ariel Sharon, a day after meeting with Abbas. Rice is talking to both sides about implementation of the road map.
Israel Army Radio said Rice and Sharon discussed details of Israel's troop pullback and an easing of restrictions, including a release of Palestinian prisoners and the possible rebuilding of the Palestinians' international airport in southern Gaza. Israeli troops destroyed the runway in 2001.
During Saturday's meeting, Rice invited Abbas to the White House in the coming days, and he accepted, a senior Palestinian official said, speaking on condition of anonymity. The White House did not immediately confirm the invitation.
Abbas would be the first Palestinian leader in three years at the White House. President Bush has boycotted Arafat, saying he is tainted by terror, while Sharon has met repeatedly with the president.
Palestinian Cabinet Minister Yasser Abed Rabbo said the Palestinians told Rice of the importance of getting Israel to halt attacks against militants and release prisoners, including Barghouti. "We told her that this would create a positive atmosphere to implement the road map," the cabinet minister said.
As part of the U.S.-backed peace plan, Israel and the Palestinians agreed on the handover of security responsibility to the Palestinians in the Gaza Strip and the West Bank town of Bethlehem. Israel insists that the Palestinians must halt terror attacks originating in the areas they control.
On Sunday evening, Israel TV showed pictures of a long line of vehicles snaking northward out of the strip. Israeli forces moved into the area of the town of Beit Hanoun several weeks ago, attempting to halt Palestinian militants from firing rockets at an Israeli town just outside the Gaza fence.
As a key element of the agreement, Palestinians are to be allowed freedom to travel the length of the main road in Gaza, cut often in two places by Israeli forces as a response to attacks against Israeli settlers in the narrow strip.
Israel sealed crossing points from Palestinian territories at the start of fighting, nearly three years ago, preventing more than 100,000 Palestinians from reaching jobs inside Israel.
The security deal, negotiated by Palestinian security chief Mohammed Dahlan and Israel's Maj. Gen. Amos Gilad, came with an Israeli pledge to halt targeted killings of wanted Palestinians — a key militant demand 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 Israel has reserved the right to go after assailants themselves if Palestinians do not.