A ceasefire aimed at halting months of deadly internal Palestinian violence held on its first day, but underlying tensions cast doubt on the future of the stand-down.

For the most part, gunmen from the rival groups Hamas and Fatah held their fire on Tuesday, observing a truce that went into effect before dawn. In the only exception, a Hamas militant was killed in the southern city of Khan Younis. Hamas blamed Fatah but did not retaliate.

Palestinian Prime Minister Ismail Haniyeh of Hamas called for a total halt to the internal violence that killed 36 people over the past week alone.

"The past few days were difficult, and everyone paid in blood," he said in Gaza. "Everyone is facing a difficult test, either we maintain this calm ... or everything collapses again, and then everyone will be held responsible."

Previous truce deals between Hamas and Fatah militants in Gaza have quickly collapsed into new waves of fighting, and it appeared unlikely the two sides would comply with all the terms of the current agreement, such as handing over all those involved in killings.

Late Tuesday, the two sides began releasing hostages -- fighters kidnapped over the past week -- both sides said.

Hamas and Fatah gunmen have used prior lulls to prepare for the next round of fighting.

After meeting Tuesday with top military officials to discuss the Monday suicide bombing in Eilat, Israeli Prime Minister Ehud Olmert decided to refrain from launching large-scale attacks in Gaza and to continue to observe a two-month-old cease-fire with the Palestinians, Israeli media reported.

The internal Palestinian fighting began to die down before dawn Tuesday. However, the truce agreement did nothing to resolve the underlying power struggle between Hamas and Fatah that has fueled the fighting. The two sides have been at odds since Hamas defeated Fatah in legislative elections a year ago, dividing power in the Palestinian government.

Palestinian President Mahmoud Abbas of Fatah, elected separately two years ago, has urged Hamas, which faces international isolation because of its anti-Israel ideology, to join Fatah in a more moderate coalition. He hopes a softer platform will help end a crippling international aid boycott imposed after Hamas' victory and allow him to resume peace talks with Israel.

Coalition talks have broken down and appear unlikely to resume soon, though both Saudi Arabia and Egypt have offered to mediate.

Saudi Foreign Minister Saud al-Faisal on Tuesday urged Abbas and Haniyeh to accept an invitation to a Saudi-mediated reconciliation meeting in Mecca aimed at resolving the crisis. Haniyeh and Abbas have both welcomed the Saudi invitation, but added that a truce must hold before such a meeting can be convened.

Foreign Minister Mahmoud Zahar of Hamas said the truce agreement calls for security forces to return to their bases, suspects in killings to be handed over, and all hostages to be released. Hamas and Fatah representatives met Tuesday with Egyptian mediators to discuss implementing the more contentious parts of the deal.

Both Fatah and Hamas say bringing suspects to trial is crucial to maintaining the truce.

"If the killers remain in the streets, the cycle of bloodshed will not stop," said Maher Mekdad, a Fatah spokesman. "Families of victims will take the law in their own hands, and revenge will rule."

In Egypt, Abbas called for a Hamas militia known as the Executive Force to be dismantled, calling it "illegitimate and illegal." Some of its members can be absorbed into the current security forces, he said. Much of the recent fighting was between the militia and the Fatah-dominated Palestinian security forces.

Haniyeh said Tuesday he supported reformulating the security forces to include Hamas members, but stopped short of saying he would disband the militia.