More than 100 people have died in the Gaza Strip in six days of violence, Hamas officials say, as Israeli forces continue a bombardment they say aims to stop rocket attacks into Israel.
Monday's fatalities include a commander of the Islamic Jihad militant group.
More than 100 rockets were fired on Israel by militants on Monday. Three Israelis have died since Wednesday.
Efforts to secure a ceasefire continue, with a senior Egyptian official saying there are "encouraging signs".
UN Secretary-General Ban Ki-Moon has arrived in Cairo to aid negotiating efforts. He plans to meet Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas in the coming days.
US President Obama spoke to his Egyptian counterpart Mohamed Mursi and to Mr Netanyahu on Monday and "discussed ways to de-escalate the situation in Gaza," the White House said in a statement.
Mr Obama "underscored the necessity of Hamas ending rocket fire into Israel" in his call to Mr Mursi, and "expressed regret for the loss of Israeli and Palestinian civilian lives" in both calls.
Khaled Meshaal, the political leader of the Islamist movement Hamas which controls Gaza, said Mr Netanyahu had requested a ceasefire but that it was up to Israel to stop the war that, he said, it had started.
Israel immediately denied making any such request.
"Hamas's comments about a ceasefire, alleging that Israel is begging for one, are about as accurate as its claims to have shot down an F-15 [warplane] or attacked the Knesset," Reuters news agency quoted a senior government official as saying.
Mr Meshaal said that a truce was possible in Gaza - as was further escalation of the conflict.
Mr Meshaal said Hamas' conditions for a truce included lifting the Israeli blockade on Gaza and an end to "Israel's assassinations".
Israel has also presented conditions for a ceasefire, which include no hostile fire of any kind from Gaza and international efforts to prevent Hamas from rearming.
Meanwhile, Turkish Prime Minister Recep Tayyip Erdogan described Israel as a "terrorist state", citing the "massacre of children" during its bombardments of Gaza.
Once cordial relations between Turkey and Israel soured after Israeli marines stormed a Turkish aid ship in 2010 during a naval blockade of Gaza.
Hamas officials gave details of several fatalities during Monday afternoon which pushed the Palestinian death toll above 100.
A leading figure in the militant group Islamic Jihad, named as Ramez Harb, was killed as a building housing media workers was struck.
Six others were killed in four separate attacks, AFP quoted emergency services as saying, and four people died of injuries sustained on Sunday.
Gaza militants launched more than 100 missiles into Israel on Monday, said the IDF. There are no reports of casualties.
At least nine children were killed in Gaza on Sunday - the bloodiest day so far - and TV reports showing images of their burned and bloodied bodies have been fuelling Palestinian anger, says the BBC's Jon Donnison in Gaza City.
In one strike, nine members of the family of Hamas policeman Mohamed Dalou were killed - four of them children.
The army's chief military spokesman, Yoav Mordechai, told Israel's Channel 2 TV that the intended target of the strike had been Yehiya Rabiyah, the head of Hamas's rocket-launching unit, but admitted that there had been civilian casualties.
Later, the IDF told the BBC that the house had been targeted because it was thought Mr Rabiyah might be hiding there, but officials did not know whether he was inside at the time of the attack.
War or peace?
Egypt has been leading efforts to broker a peace deal, with both senior Israeli and Hamas officials in Cairo for talks. An Egyptian official said he hoped to be able to make an announcement on Monday or Tuesday.
The BBC's Middle East editor, Jeremy Bowen, says it is feared the conflict might get worse before any truce is agreed.
Mr Netanyahu said on Sunday that he was ready to expand the operation, after Israel authorised the mobilisation of up to 75,000 army reservists.
Since the conflict began, 877 rockets have been fired towards Israel, the IDF says, with 570 landing in Israel and 307 intercepted by the Iron Dome missile defence system.
Before the recent offensive, Israel had repeatedly carried out air strikes on Gaza as Palestinian militants fired rockets across the border.
But the aerial and naval bombardment is its most intense assault on the territory since Israel launched a full-scale invasion four years ago.
Hamas seized control of Gaza in 2007, a year after winning a decisive victory in general elections. Israel withdrew from the strip in 2005 but maintains a blockade around it.
Israel, as well as the United States and the European Union, regards Hamas as a terrorist organisation.