Fighting between Hamas and Israel continued on Sunday despite a series of ceasefire announcements by both sides, each of which was rejected by the other amid mutual blame and recrimination.
There was no sign of a longer-term deal to end the military confrontation, which began three weeks ago on Tuesday and which has claimed about 1,100 lives, the vast majority of them Palestinian civilians. The US secretary of state, John Kerry, returned to Washington at the weekend after his efforts to forge a ceasefire agreement between the two sides failed.
US president Barack Obama, in a phone call to Israel's prime minister Binyamin Netanyahu, stated his concern at the rising number of civilian deaths and urged an immediate, unconditional ceasefire.
Rockets were launched from Gaza and Israel carried out air strikes in the hours following a Hamas call for a 24-hour humanitarian ceasefire from 2pm on Sunday.
Hamas said its pause was for Eid al-Fitr, which marks the end of Ramadan and is the most important holiday in the Muslim calendar. In Gaza City, people ventured out to stock up on food and essentials for the three-day holiday, which starts on Monday.
"In response to UN intervention and considering the situation of our people and the occasion of Eid, it has been agreed among resistance factions to endorse a 24-hour humanitarian calm, starting from 2pm on Sunday," Sami Abu Zuhri, a Hamas spokesman, told Reuters.
Israel, however, rejected the call, and Netanyahu, later said the militants had "violated even their own ceasefire".
"They are shooting at us as we speak," he said in a series of interviews on US television networks, adding: "Under these circumstances, Israel will do what it must do to defend its people."
Israel's security cabinet was meeting on Sunday evening to discuss the next steps.
Khaled Mishal, Hamas's leader in exile, told PBS that Israel must end its occupation. "We are not fanatics. We are not fundamentalists. We are not actually fighting the Jews because they are Jews per se. We do not fight any other races. We fight the occupiers," he said.
The weekend saw a confusing sequence of unilateral ceasefires, starting with a 12-hour lull in Israeli military action on Saturday in response to a UN call. Hamas did not formally sign up to the ceasefire, but refrained from rocket fire for its duration. Israel later extended the ceasefire by four hours to midnight on Saturday, then said it would withhold fire for a further 24 hours until midnight on Sunday. It resumed attacks on Sunday morning, however, in response to rocket fire from Gaza. Hamas's unilateral ceasefire announcement came shortly afterwards.
Warning sirens sounded over southern Israel, however, and the Israeli military reported that its missile defence system, Iron Dome, had shot down at least eight rockets in Be'er Sheva and Kiryat Gat. A rocket hit a house in the south, slightly injuring a woman.
In Gaza, one person was killed when a vehicle carrying workers to fix water pipes was hit in an air strike, the Palestinian Red Crescent said. Shells were fired from tanks and naval boats, according to reports.
An immediate obstacle to an agreed ceasefire centres on dozens of cross-border tunnels that Hamas has constructed. Israel has insisted its forces must be allowed to continue to search and destroy the tunnels during any pause in the fighting. Hamas is unlikely to agree to a continued Israeli military presence inside Gaza.
There are also wide gaps between each side's demands concerning a longer-term ceasefire. Israel wants to see the demilitarisation of Gaza, including measures to prevent Hamas and other militant groups from rearming.
Hamas wants the seven-year siege of Gaza to be lifted, with crossings to both Israel and Egypt opened, plus the release of Palestinian prisoners in Israeli jails.
The death toll in Gaza rose to more than 1,030 on Sunday. Unicef said 218 children had been killed. Two-thirds were under the age of 12, it added.
The Israeli Defence Forces said 43 soldiers had died. Two Israeli civilians and a Thai agricultural worker were killed in rocket attacks.
Last night, Israel acknowledged that a "single, errant" mortar shell landed in the courtyard of a Beit Hanoun school last week but claimed – to much criticism - that surveillance pictures showed it was empty at the time.
The Gaza health ministry said hospitals were running out of beds, with patients ready to be discharged unable to leave because they had nowhere safe to go.
"From the human point of view we can't force them out," said Sobhi Skaik, the medical director of the Shifa hospital in Gaza City.
"A patient is not just a medical problem. Their social and economic aspects are also important. The medical staff are always trying to work with the patients to find solutions."
Many families of the injured were camping in the grounds of the Shifa, the largest public hospital in Gaza, he added.
"The hospital grounds have become like a refugee camp. The conditions are deteriorating, with rubbish piling up. It is quite dirty and unsanitary, and we cannot discharge our patients into those conditions."
In Jerusalem, two Palestinians were in hospital after about a dozen Israeli Jews allegedly attacked them with iron bars amid continuing tensions in the city. Police said they were investigating the claim.
Israeli police said they had thwarted an attack when they stopped a car containing explosives at a checkpoint between the West Bank and Jerusalem.
Clashes in the West Bank between Palestinians protesting at the war in Gaza and Israeli forces appeared to subside after 10 youths were shot dead at the weekend. About 600 people were injured, many by live gunfire.
In Rome, Pope Francis made an appeal for an end to bloodshed around the world, without making specific reference to Gaza. "Stop, please stop! I beg you with all my heart," he said in the weekly Angelus prayer.