Foreign Secretary Philip Hammond has repeated Britain's call for an "immediate and unconditional humanitarian ceasefire" in Gaza when he spoke by phone to two senior ministers from Benjamin Netanyahu's government.
Mr Hammond welcomed indications that Israeli troops may soon be withdrawn from the Palestinian enclave, following an incursion which has lasted 27 days, but told foreign minister Avigdor Lieberman and justice minister Tzipi Livni he was "appalled" by the deaths of civilians near a United Nations school in Rafah.
The talks came as Ed Miliband hit out at David Cameron for failing to make clear to Israel the extent of British public concern at the suffering in Gaza.
Downing Street responded sharply last night after Mr Miliband accused the Prime Minister of an "inexplicable" silence over the suffering of Palestinian civilians, who make up the bulk of the 1,700 killed during the Israeli offensive.
A spokesman for Number 10 responded: "The Prime Minister has been clear that both sides in the Gaza conflict need to observe a ceasefire. We are shocked that Ed Miliband would seek to misrepresent that position and play politics with such a serious issue."
But Mr Miliband returned to the fray today, suggesting that Mr Cameron was out of step with public feeling in the UK. The Labour leader said: "The Government needs to send a much clearer message to Israel that its actions in Gaza are unacceptable and unjustifiable.
"What I want to hear from David Cameron that he believes that Israel's actions in Gaza are wrong and unjustified, and we haven't heard that from him. I think that's what the British public are thinking as they are seeing these tragic events unfolding on our television screens."
Following his talks with Mr Lieberman and Ms Livni, Mr Hammond said: " I reiterated the UK's position on the need for an immediate and unconditional humanitarian ceasefire, for every effort to be made to prevent further civilian casualties.
"Hamas must also cease the firing of rockets at Israeli communities and endangering the lives of the Israeli population.
"I welcome indications that Israeli forces may begin to withdraw from Gaza within the next few days."
The Foreign Secretary also commented on reports that 10 civilians were killed and 35 wounded by an Israeli strike at a UN school in Rafah which was being used as a shelter for displaced people.
"I am appalled at reports of further civilian casualties in the vicinity of a UN-run school housing Palestinians displaced by the Gaza conflict in Rafah this morning," said Mr Hammond. The facts are not yet clear, but it is tragic that there are further losses of life in a place which is being used as a shelter."
He added: " It's vital that we find a way forward that is enduring and any solution would need to provide genuine stability, and not simply lead to a repeat of the cycle of violence.
"In order to be sustainable, any ceasefire agreement needs to show a clear path to real change in Gaza for the future if we are to avoid future conflict and improve life for ordinary Gazans as well as address Israel's legitimate security needs."
Meanwhile, Deputy Prime Minister Nick Clegg - who has previously said that Israel's actions "appear disproportionate" - called for an immediate end to the violence.
Speaking in Edinburgh, Mr Clegg said: " It is so important not only to stop this terrible humanitarian catastrophe in Gaza itself, with hundreds upon hundreds of innocent civilians being killed, but also for the long-term security of innocent Israeli civilians who have been subject to these unacceptable rocket attacks.
"It is essential for everybody on all sides of this conflict that this outburst of military violence must now cease."
Large swathes of Gaza have been destroyed, more than 8,000 Palestinians have been wounded and some 250,000 people have been forced to flee their homes since Israel began its operation to prevent Hamas missile strikes into its territory and block tunnels used to launch raids across the border.
Israel has lost 64 soldiers and three civilians in the conflict, its highest death toll since the 2006 Lebanon war.
Among the dead was Second Lieutenant Hadar Goldin who was initially reported to have been captured by Hamas on Friday, but now appears to have been killed in battle early that day, said Israel's military. The 23-year-old infantry officer is understood to have spent some years living in Cambridge.
In a televised address late yesterday, Mr Netanyahu suggested troops would reassess operations after completing the demolition of Hamas military tunnels under the border. Security officials said the tunnel mission was winding down.
At the same time, Mr Netanyahu warned the territory's Hamas rulers that they would pay an "intolerable price" if militants continued to fire rockets at Israel and that all options remain on the table.
Hamas has said it will not stop fighting until Israel and Egypt lift their blockade of Gaza, imposed after the Islamic militant group took control of the territory in 2007.