Palestinians have fleed from their homes in Gaza as Israeli officials say their cabinet can halt its three-week-old Gaza offensive.
Exhausted by lack of sleep, shattered by countless bombs and drained by bereavement, Gazans held out hope to end Israeli offensive in Gaza on Saturday under a ceasefire, if only for a chance to collect their lives.
Hamas offers a one-year, renewable truce on condition that all Israeli forces withdraw within a week and that all the border crossings with Israel and Egypt are opened.
The security cabinet is due to meet at 7.30 p.m. (1730 GMT) and Prime Minister Ehud Olmert will address the nation at 10 p.m.
"We do not care how, we want a ceasefire. We want to go back to our homes. Our children need to go back to sleep in their beds," said Ali Hassan, 34, a father of five who is sheltering in his brother's house in the centre of Gaza.
Palestinians say unilateral ceasefire from Israel was not solution for the Gaza Strip.
"Israel could claim they entered the heart of Gaza, destroyed the places, killed Seyyam and can come again any time," Hasan said, referring to Hamas security chief Saeed Seyyam, who was killed by an Israeli air strike on Thursday.
"Enough is enough," he said, explaining how he had moved his family from north Gaza to the centre of the city two weeks ago to escape Israeli bombardments in his neighbourhood.
"Our ears were about to blow up from the continued bombings. We are even lucky to be alive still," he said.
Despite stepped-up diplomacy and signs a ceasefire could soon be declared, Israel has sustained its three-week-old air, tank and artillery assault.
In the face of the onslaught, which Palestinian doctors say has killed 1,200 Palestinians, including 410 children, Israel has continued its bombardment
Thirteen Israelis have been killed in the conflict, 10 soldiers and three civilians hit by rocket fire.
With several relatives killed, Hassan suggested it was time for Israel to take the initiative and cease fire.
"I have always been a supporter of rockets and all forms of resistance," said Aziz, the taxi driver. "But maybe Hamas needs to renew martyrdom operations instead," he said, referring to suicide attacks.
Hassan, the father of five, said there was little point in firing rockets if they were not effective.
"Rockets -- I think this issue needs to be stopped for sometime and restudied," he said. "Once we have a missile that can reach the heart of Tel Aviv and blow up a building, maybe they can resume fire."
"It was a real second exodus"
Residents of a Gaza neighbourhood devastated by Israeli assault fled to other parts of the enclave on Friday, showing little faith in prospects for ceasefire talks.
For some it recalled the refugee exodus of 1948, when Palestinians fled or were forced out of what became Israel. Many of them ended up in Gaza, where they and their families now form the majority of the population of 1.5 million.
People loaded mattresses, suitcases and other belongings onto cars in Tel al-Hawa, an affluent and once quiet district of the city of Gaza where buildings were damaged by Israeli troops on Thursday, the 20th day of Israel's offensive.
"We will never forget this night. We never imagined we'd emerge alive," said Abu Mahmoud, a 54-year-old father of five who refused to give his full name.
Abu Mahmoud said his family spent the night on a small rug in the building's staircase where they huddled up together to the sound of explosions and machinegun fire.
"We've never been so close to death," he said, adding that the ordeal brought to mind his parents' account of 1948.
In that year, Israel was established and much of the Arab population fled or were driven from their homes -- most Gazans are from families of those refugees from what is now Israel.
"It was a real second exodus," said Abu Mahmoud.
Gazans who escaped the fighting in Tel al-Hawa returned to buildings disfigured by shells and bullets and streets littered with debris.
People chatted in the streets, happy to see their neighbours and friends alive.
Human Rights Watch called on Israel to stop firing heavy artillery shells at residential areas of the city of Gaza, saying the practice was in violation of international law.