Hamas announced a ceasefire of its rocket attacks on southern Israel yesterday, in a move which it said was independent of the Israeli earlier on Sunday. The truce is fragile but there are hopes that it can be consolidated.
Hamas' deputy chief in Syria, Moussa Abou Marzouk, said the cessation was in the name of all "Palestinian resistance factions".
He declared: "We... announce a ceasefire of our factions in the Gaza Strip and we stress that our demand is the withdrawal of the enemy forces from the Gaza Strip within a week, along with the opening of all the crossings for the entry of humanitarian aid, food and other necessities for our people in the Gaza Strip."
Hamss said the ceasefire would be temporary unless Israel met these long-standing demands. Israel has made a similar pledge in relation to militant rocket attacks.
In a televised speech, the top Hamas leader in Gaza, Ismail Haniya, said the Palestinian people had won a great victory over Israel and that the three-week offensive had not cowed the Palestinians.
Israel's foreign affairs spokesperson told the BBC that their troops would be withdrawn from the Gaza Strip "in good time" if there was "a total halt to attacks by Hamas".
The BBC's Bethany Bell, on the Israeli side of the border with Gaza, says Israeli helicopters and drones have been flying overhead and Israeli troops are on high alert.
Commentators say that while both Israel and Hamas are claiming victory for their goals, in reality both sides have failed to gain any decisive advantage - at great cost to life and limb, especially on the Palestinian side, given Israel's overwhelming military might.
Meanwhile, Pope Benedict used his Sunday prayers to denounce violence on both sides, without directly naming either of them.
The pontiff told those gathered in Saint Peter's Square to pray for the hundreds of children, elderly, women who have fallen as "innocent victims of unheard of violence".
He wished success on all efforts "to end the tragedy" in Gaza and bring about lasting peace. He was speaking just hours before a summit on the crisis at Sharm El-Sheik, in Egypt.
The pope said he wanted to encourage those who believe there is room for everyone in the Holy Land. He expressed the hope that all sides could help their populations pick themselves up from the ruins and the terror and bravely pick up again the thread of dialogue, in justice and in truth.
Pope Benedict sent aid on 17 January to the Gaza Strip for Catholics there to distribute to victims of the conflict.
The 22-day-long campaign to stop Hamas firing rockets into Israeli territory has killed at least 1,300 people, including more than 400 children. Large areas of Gaza are now in ruins. Thirteen Israelis have died.