The Palestinian Authority has released a Hamas militant who was arrested in Gaza overnight following a gun battle.
Hamas has refused to disband under the roadmap peace plan
The arrest sparked tension between the Palestinian security forces and Hamas, and Egyptian officials were called in to mediate a solution, Hamas said.
The PA said its forces exchanged fire with three Hamas men suspected of trying to fire missiles at a Jewish settlement or a nearby Israeli town.
Hamas denied preparing an attack and called for protests over the arrest.
The message for Hamas supporters to take to the streets was broadcast from mosques' loudspeakers.
Risk of unrest
The BBC's Alan Johnston in Gaza says the events on Monday night show that any attempt by the PA to enforce the ceasefire by confronting the powerful, well-armed Hamas movement risks sparking serious unrest.
Hamas has not endorsed the truce, but it has agreed to rein itself in. The movement has launched occasional attacks in response to what it says have been Israeli army truce violations.
About 16 Palestinians have been killed in Gaza since the ceasefire came into force in February.
The incident, near the northern town of Beit Lahiya, coincided with renewed Israeli calls for Palestinian leader Mahmoud Abbas to disarm militants under the terms of the international peace plan known as the roadmap.
"There will be no new transfer of control as long as the question of the wanted terrorists is not addressed by the Palestinian Authority, which has not disarmed them," Defence Minister Shaul Mofaz told Israeli public radio.
Israel has agreed in principle to hand security control for five West Bank towns back to the Palestinians, but so far only two transfers have taken place, in Jericho and Tulkarm.
Prime Minister Ariel Sharon has told two senior US politicians visiting Israel that Mr Abbas was not taking significant steps to tackle hardline groups.
"Instead of disbanding the terrorist organisations, he is acting to strengthen them. He is not willing to fight them and is similarly unwilling to disband their infrastructures," Mr Sharon said.
An Israeli soldier and a member of Islamic Jihad died in a shootout near Tulkarm on Monday.
The incident came after the Israeli military entered the area for the second day in a row.
Islamic Jihad said it carried out a rocket attack from Gaza at the Israeli town of Sderot in retaliation.
The rocket attack came shortly before the Palestinian security forces confronted the Hamas patrol - and correspondents say they may have mistakenly believe the patrol was responsible.
A Palestinian security official said police found rockets in the vehicle the Hamas men were using.