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.
Downing Street said Mr Cameron spoke to Israeli prime minister Benjamin Netanyahu by telephone on Thursday night to discuss the situation following Israel's assassination of Ahmed Jabari, the Hamas military chief, in a drone strike on his car on Wednesday.
Referring to Mr Cameron's conversation with his Israeli counterpart, a Downing Street spokesman said: "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 spokesman added: "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 Friday 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 Hague said: "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. The rocket attacks also risk worsening the plight of Palestinian civilians in Gaza, which is already precarious.
Daniel Taub, the Israeli ambassador to the UK, said Hamas needed to accept "some basic ground rules", which meant acknowledging the right of Israel to exist and renouncing violence.
Speaking on ITV's Daybreak, he said: "It is hard to think of Israel as a thug because really what characterises Israel's behaviour over the last 10 years is astonishing restraint. Ideally what we want to see is a peace treaty. That's why we have been trying to deal with the Palestinian Authority in Ramallah, where we have been saying 'come to the negotiating table'. Unfortunately in Hamas in the Gaza Strip we have a group that is hell-bent on the destruction of Israel."