Hamas said on Sunday it would cease fire immediately along with other Islamist resistance groups in Gaza to give Israel, which already declared a unilateral truce, a week to pull its troops out of the territory.
A spokesman for Israeli Prime Minister Ehud Olmert said earlier that if a ceasefire held in the Hamas-ruled enclave, Israel could start the process of withdrawing its forces.
"Hamas and the factions announce a ceasefire in Gaza starting immediately and give Israel a week to withdraw," said Ayman Taha, a Hamas official in Cairo for talks with Egypt on a truce deal.
Hamas's exiled leadership confirmed the immediate ceasefire in a statement.
"We are ready to cooperate with any efforts, especially Egypt... to reach a definite agreement that meets our known demands to lift the blockade permanently and open all border crossings," the statement said.
Palestinians rushed to remove bodies from rubble and survey damage to homes damaged or destroyed since Israel launched on Dec. 27 its most powerful offensive in the enclave in decades.
Israel kills one civilian
Earier on Sunday, an Israeli aircraft attacked rocket launchers in the Gaza Strip on Sunday killing one Palestinian after Hamas fighters fired salvoes into southern Israel and Israel returned fire, puncturing a tenuous unilateral ceasefire in the war that has killed 1,207 Palestinians, more than half of them women civilians and children.
In south Gaza, a 20-year-old man became the first Palestinian killed since the truce went into effect when Israeli troops shot him in the chest while he travelled in a vehicle near the southern town of Khan Yunis, medics said.
As the army carried out its first air raid on militants firing rockets, Prime Minister Ehud Olmert warned that the unilateral truce Israel had begun hours earlier was fragile and was being constantly reassessed.
"The government's decision allows Israel to respond and renew the fire if our enemy in the Gaza Strip continues its strikes," he said at the start of the weekly cabinet meeting in Jerusalem.
"This morning they again proved that the ceasefire is fragile and it has to be reassessed on a minute by minute basis," he said. "We hope that the fire ends. If it continues, the IDF (Israeli Defence Forces) will respond. It is prepared and deployed to do so."
In the first reported violence after the ceasefire went into effect, Hamas gunmen shot at Israeli troops near Jabalya refugee camp, an Israeli military spokesman said.
Hamas sources said there had been a brief clash with Israeli troops pulling out of Jabalya.
Unilateral ceasefire
Israel halted its 22-day-old Gaza offensive at 2 a.m. (0000 GMT), saying it had achieved all its objectives but that a troop withdrawal was contingent on Hamas ceasing its fire completely, with no timetable being set.
Hamas said it would not accept the presence of Israeli soldiers in the Gaza Strip and would "continue to resist them." Israeli leaders said the military would respond strongly if Hamas kept up attacks.
Olmert cited internationally backed understandings with Egypt, Gaza's southern neighbor, on preventing Hamas from rearming through smuggling tunnels as a reason behind Israel's decision to call off its attacks.
Egypt's President Hosni Mubarak invited European leaders to a hastily called summit on Sunday to try to bolster the unilateral truce although Israel had sidestepped Cairo's efforts to achieve a negotiated end to the hostilities with Hamas.
Israel launched air strikes on the Gaza Strip on Dec. 27 and ground troops pushed into the enclave a week later, saying its main aim was an end to the rocket fire that had killed 18 people in Israel over the previous eight years.
War tally
At least 1,207 Palestinians, including 410 children, have been killed since the start of Israel's deadliest-ever assault on the territory, according to Gaza medics, who said another 5,300 people have been wounded.
Those slain in the war also include 109 women, 113 elderly people, 14 paramedics, and four journalists, according to Dr. Muawiya Hassanein, the head of Gaza emergency services.
Ten Israeli soldiers and three civilians hit by rockets were killed since the start of the. The army said more than 700 rockets and mortar rounds have been fired into Israel during that period.
In the hours leading up to the security cabinet meeting, Israel kept lobbing shells into the densely populated urban area, while to the north in Beit Lahiya a U.N.-run school was set ablaze by bombs.
Two brothers, aged five and seven, were killed and another dozen people wounded in the attack, in which burning embers trailing smoke rained down on a school where some 1,600 people were sheltering, setting parts of it alight.
Ban called the fourth such attack on a U.N.-run school during the war "outrageous" and demanded a thorough investigation.
During the course of the war, schools, hospitals, U.N. compounds, media outlets and thousands of homes all came under attack with the Palestinian Authority putting the cost of damage to infrastructure alone at $476 million.
The halt to the violence came after the Jewish state won pledges from Washington and Cairo to help prevent arms smuggling into Gaza, designated to form part of the Palestinians' promised future state, along with the larger West Bank region.
The ceasefire comes less than a month before Israel holds elections when Olmert, who formally resigned last autumn, is due to stand down.