More than 20 members of one family killed in Gaza strike

'We don't want to see any more civilians killed' says Barack Obama as IDF attacks intensive care unit in day of bloodshed

A hospital was shelled, killing and injuring staff and patients, and up to 28 members of one family died in an air strike as Gaza endured another day of relentless bloodshed on Monday .

As heavy shelling and fighting on the ground continued, the US president, Barack Obama, restated his call for an immediate ceasefire, saying: "We don't want to see any more civilians killed."

He said he had authorised his secretary of state, John Kerry, to do "everything he can to help facilitate a cessation of hostilities" in a sign that international diplomacy had been galvanised by the weekend carnage in Shujai'iya.

Kerry was en route to Cairo for urgent talks with key players in the region, including the UN secretary-general, Ban Ki-moon. The UN security council called for an immediate ceasefire on Sunday.

In Deir al-Balah in central Gaza, al-Aqsa hospital became the third to be struck in the 14-day conflict when three shells slammed into the intensive care unit, surgical and administrative areas.

Five people were killed and 70 wounded, including about 30 medics, according to Gaza health officials. Ambulances tried to evacuate patients but were forced to turn back by continued shelling. Israel has claimed that Hamas hides weapons in hospitals.

Further south, in Khan Younis, an extended family was wiped out in an air strike on a house. The number of dead was put at between 24 and 28. The Palestinian Centre for Human Rights said another 10 people were killed in a single air strike in Rafah, including four young children and a baby.

Save the Children said that, on average, seven had been killed every day during the conflict. "For many children, this is the third war in six years that they are going through," said the charity's David Hassell.

Israeli troops said they killed 10 Hamas militants as they attempted a cross-border attack using two tunnels. The Israel Defence Forces said seven soldiers had been killed in the 24 hours up to early evening.

Intense rocket fire from Gaza continued, with sirens warning people in Tel Aviv and other towns in central and southern Israel to seek shelter. The IDF continued to say it was investigating Hamas claims that it captured an Israeli soldier on Sunday. Hamas displayed a photo ID, saying the soldier's name was Shaul Aron. Street celebrations erupted in Gaza at the news, with people chanting "Allahu Akbar" and lighting fireworks. If the capture of an Israeli is confirmed, it will complicate efforts to broker a ceasefire.

"We advise [Israel] to take their soldiers and leave before we kidnap more soldiers in addition to the scores we have already killed and wounded," said Hamas spokesman Sami Abu Zuhri.

The number of Palestinians killed in the conflict reached 530 by early evening, 72% of whom were civilians according to the UN. Twenty-seven Israelis – 25 soldiers and two civilians – have died. The UN said more than 100,000 people have fled their homes, including 85,000 people who sought shelter in schools.

Ten Israeli human rights organisations have written to the attorney-general to raise concerns about grave violations of international law in the conflict. They questioned the legality of Sunday's operation in Shujai'iya, "in particular, the potential violation of the fundamental principles of the laws of war, specifically the principle of distinguishing between combatants and civilians".

Israel's prime minister, Binyamin Netanyahu, the defence minister, Moshe Ya'alon, and chief of staff, Benny Gantz – the men directing the military operation in Gaza – said in a statement it would expand and continue "as long as necessary until the completion of the task". Israel has said the goal of the ground invasion is to locate and destroy dozens of tunnels under the border, used by militants to launch attacks.

In Cairo, Ban held talks with Egyptian president Abdel-Fattah al-Sisi and the head of the Arab League. The Palestinian president Mahmoud Abbas was due to meet Hamas's leader-in-exile Khaled Mishal in Doha.

Egypt's proximity to Gaza, its peace treaty with Israel and good relations with the western-backed Palestinian Authority in the West Bank have made it the focus of attempts to defuse the crisis, though its relations with Hamas – which it sees as an offshoot of the banned Muslim Brotherhood – are hostile.

Hamas rejected Cairo's original ceasefire proposal last week, though a senior official said Egypt might be willing to amend its initiative. "Egypt does not mind adding some of Hamas's conditions provided that all involved parties approve," the official told Reuters. Hamas is demanding an end to the blockade of Gaza, an end to hostilities, opening the border to Egypt, the release of prisoners held by Israel and other conditions – in exchange for a truce.

Ismail Haniyeh, the former Hamas prime minister, claimed that Israeli forces were being beaten in Gaza. "The Palestinian resistance will meet the demands and expectations of the Palestinian people," he said, adding that the Hamas conditions were "the minimum demands" for any truce.

"Our people's sacrifices are heading for triumph," he said in a pre-recorded TV broadcast. "We see the al-Qassam Brigades and the Jerusalem Brigades and all resistance factions beating the enemy and attack him again and again, under the earth and sea. The ground operation is a declaration of failure on the part of the enemy aerial war against Gaza."

Mishal was due to speak later, fuelling speculation about a possible "victory" speech that could pave the way for acceptance of a ceasefire. © Guardian News and Media 2014