Hamas bears "principal responsibility" for the escalating crisis between Gaza and Israel, Downing Street has said.
Number 10 also called rocket attacks on Israel by Hamas "completely unacceptable". It said Prime Minister David Cameron was "extremely concerned" by the escalation in violence.
Number 10 said Mr Cameron spoke to Israeli prime minister Benjamin Netanyahu by telephone to discuss the situation following Israel's assassination of Ahmed Jabari, the Hamas military chief, in a drone strike on his car on Wednesday.
A Downing Street spokesman said: "The Prime Minister spoke to the Israeli Prime Minister, Benjamin Netanyahu, this evening to discuss the situation in Gaza and southern Israel. The Prime Minister said that he was extremely concerned by the dangerous situation and deeply sorry for the loss of civilian life on both sides.
"He said the rocket attacks from Gaza into southern Israel by Hamas and other armed groups were completely unacceptable and that the increasing frequency of rocket attacks in recent days was the immediate cause of the situation. He made clear that Hamas bears the principal responsibility for crisis.
"The Prime Minister said that the priority must be to de-escalate the crisis. He called on Mr Netanyahu to do all he could to avoid civilian casualties and emphasised that both sides needed to avoid a spiral of violence that would be in no-one's interest, particularly at a time of instability in the region."
Downing Street said the Prime Minister hopes to speak to the president of Egypt, Mohammed Morsi, on Thursday on the same issue.
Earlier, Foreign Secretary William Hague urged Tel Aviv to reduce tension and avoid civilian casualties but he stopped short of demanding an end to its air strikes. The intervention came amid a fresh wave of bloodshed following an Israeli attack that killed the leader of Hamas's military wing. Mr Netanyahu has warned that his country is prepared to extend its operation against Hamas, sparking fears of a repeat of the ground incursion four years ago in which hundreds died.
"I utterly condemn rocket attacks from Gaza into southern Israel by Hamas and other armed groups. This creates an intolerable situation for Israeli civilians in southern Israel, who have the right to live without fear of attack from Gaza," Mr Hague said. "I also strongly urge Israel to do their utmost to reduce tension, avoid civilian casualties and increase the prospects for both sides to live in peace."
The conflict has been intensifying over recent weeks, but flared up dramatically in the wake of the Israeli strikes against senior Hamas figures. Hundreds of rockets have been fired into Israel, with three people killed in the town of Kiryat Malachi - about 15 miles north of Gaza - on Thursday morning. At least 11 Palestinians, including some civilians, are reported to have died over the past two days.