More than 100 people have died in Gaza in six days of airstrikes by Israel, according to Hamas officials as diplomatic efforts continued to find ways to end the escalating conflict.
Monday's fatalities include a commander of the Islamic Jihad militant group.
President Barack Obama called Egyptian president Mohammad Morsi and Israeli prime minister Benjamin Netanyahu on Monday to discuss the ongoing violence.
Smoke rises following an Israeli attack on smuggling tunnels between Gaza and Egypt
In a statement, the White House said the president and Mr Morsi discussed ways to de-escalate the situation in Gaza whil Mr Obama also stressed the urgent need for Hamas to stop firing rockets into Israel.
British foreign secretary William Hague praised Egyptian ceasefire negotiations for averting an Israeli ground invasion so far in the Gaza crisis.
He said the fact that Israel was holding back from an invasion of Gaza, and that rocket attacks on Israel were lessening, were "positives" in an otherwise desperate situation.
Mr Hague was speaking after talks in Brussels in which EU foreign ministers voiced full support for continuing international peace efforts.
As well as the Palestinian casualties, there have been three Israelis reported killed by Israeli air strikes on Gaza which began last week in response to a wave of rocket attacks on Israeli towns and cities from the Palestinian enclave.
Mr Hague repeated Britain's position that Gaza's Hamas rulers were to blame for starting the offensive, but said Israel also had a responsibility to "de-escalate" the violence.
Leaving Brussels, he paid tribute to Egyptian efforts to negotiate "a ceasefire that can work".
He went on: "I am pleased that Israel has held back from a ground invasion while such negotiations go on, and that the rate of rocket attacks on Israel has fallen, for whatever reason, over the last 24 hours.
William Hague (right) talks with Bulgarian foreign minister Nikolay Mladenov at Monday's meeting in Brussels
"These are positive developments, but of course it remains a desperately serious and difficult situation".
Mr Hague said everyone across Europe remained gravely concerned about Gaza, and EU governments, including the UK, fully supported continuing peace efforts.
A declaration from the foreign ministers emphasised Israel's "right to protect its population" but said any response to rocket attacks from Gaza had to be proportionate.
"The European Union expresses grave concern about the situation in Gaza and Israel and deeply regrets the loss of civilian life on both sides," said a statement from the foreign ministers.
"All attacks must end immediately as they cause unjustifiable suffering of innocent civilians. It (The EU) therefore calls for an urgent de-escalation and cessation of hostilities."
The statement demanded an "urgent de-escalation and cessation of hostilities" on both sides and gave full EU support to ceasefire efforts and a UN peace mission.
Palestinians carry an injured man from a bombed building in Gaza city after the second attack on the building in two days
It went on: "There can be no justification for the deliberate targeting of innocent civilians. Israel has the right to protect its population from these kinds of attacks; in doing so it must act proportionately and ensure the protection of civilians at all times."
The EU stressed the need for all sides to fully respect international humanitarian law.
"The current situation underlines once more the urgent need to move towards a two-state solution allowing both sides to live side-by-side in peace and security. The European Union will continue working with all those with influence in the region to bring this about."
Earlier, EU foreign policy chief Catherine Ashton, who chaired Monday'ss meeting, said she had been in touch with Israel's prime minister and with the Arab League: "We need to find a long-term solution to Gaza. We have to find a way to prevent violent attacks and to bring security and peace to people in the region.
"It fits in absolutely with what the EU has consistently said about a two-state solution."
Hamas has said that Israeli prime minister Benjamin Netanyahu had asked for a truce although Israel has denied this.
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Speaking at a news conference in Cairo, Khaled Meshaal, exiled leader of Hamas, said a truce was possible but Israel must halt its strikes first and lift its blockade of Gaza.
He added that Netanyahu was concerned about the impact of a "land war" domestically because of elections in January.
Turkey's prime minister Recep Tayyip Erdogan has condemned Israel as a "terrorist state", citing the "massacre of children" during its bombardments of Gaza, the BBC reported.
Charities have expressed concern about the safety of children in the current conflict
Foreign office minister Alistair Burt has arrived in Israel for a three-day visit, during which he will also go to the Gaza Strip.
He will meet senior Israeli ministers and Palestinian president Mahmoud Abbas and prime minister Salam Fayyad.
On Monday he visited Kiryat Malachi where a rocket hit a residential building killing three Israeli civilians last week.
"I am gravely concerned about the current crisis, particularly the loss of civilian life on both sides," he said.
"Today I have seen for myself the impact of this conflict, and the terrible toll and suffering it is inflicting on families and communities across Israel. Coming here has given me a sense of what life is like for people under attack, and the appalling devastation that rockets attacks bring.
"The people in villages, towns and cities across Israel have the right to live without the constant fear of rocket attacks.
"I look forward to speaking tomorrow to President Abbas to discuss the human impact of the conflict in Gaza, where rising numbers of civilian casualties are a real cause for concern."
Meanwhile, charities have urged world leaders to enforce a ceasefire in Gaza to protect civilian lives and infrastructure.
A group of 38 charities said the international community must apply immediate pressure on the Israelis government to keep the crossings to Gaza open to allow in supplies of essential humanitarian aid, push all parties to the conflict to end violence and uphold their obligations under international law.
Nishant Pandey, of Oxfam, said:"World leaders cannot sit by while civilian casualties in Gaza and Israel continue to mount. We urgently need to enforce a ceasefire.
"The present conflict threatens to perpetuate and worsen the humanitarian impact on Palestinian civilians in Gaza of over five years of Israeli blockade and the 2008/09 Israeli military operation Cast Lead.
"It will only deepen despair, create more insecurity, and jeopardise chances for Israelis and Palestinians to reach a just and durable peace."
The agencies said it was critical that the protection of civilians was prioritised by the parties to the conflict as outlined by international humanitarian law.
"Children are already among the dead and, as always, children bear the hardest burden during military conflict.
"Save the Children urges all parties to end the violence immediately."