President Barack Obama has personally urged leaders in Turkey and Egypt to engage with Hamas over a "de-escalation" of hostilities in Gaza, while continuing to support Israeli strikes despite mounting Palestinian civilian casualties.

Speaking on board Air Force One en route to Asia, White House national security adviser Ben Rhodes blamed Hamas for the current round of violence, stating that the "precipitating factor" for Israeli air strikes were rockets fired into civilian territories from Gaza.

It comes as the Palestinian death toll continues to rise. Up to 41 Gazans, including 13 civilians, and three Israelis have been killed since the Israeli operation began. Palestinian authorities have said their dead included at least eight children and a pregnant woman.

Asked about the bombing of government buildings – including prime minister Ismail Haniyeh's offices – the US official said he wouldn't comment on "specific targeting choices" other than to say that the administration would "always underscore the importance of avoiding civilian casualties".

But Rhodes reiterated the White House view that Hamas was responsible for the latest outburst of violence.

"Just to be clear on the precipitating factor: these rockets had been fired into Israeli civilian areas and territory for some time now. So Israelis have endured far too much of a threat from these rocket for far too long, and that is what led the Israelis to take the action that they did in Gaza," he said.

He added that the US wanted the same thing as Israelis: "an end to the rocket fire coming out of Gaza".

The comments come as the White House increased its diplomatic efforts to end the violence in Gaza.

Obama has spoken to Turkish prime minister Recep Tayyip Erdogan, it emerged on Saturday, along with Egyptian president Mohamed Morsi.

Both men have the "ability to play a constructive role in engaging Hamas and encouraging a process of de-escalation", Rhodes said.

However, on Saturday, Erdogan appeared to take a different side in the conflict, despite the call from Obama. The Turkish leader on Saturday vowed support for Gaza's Palestinians in a speech at Cairo University in Egypt. He also met Morsi for the first time since the Eggyptian Islamist leader was elected in late June, with Erdogan saying that that win at the polls offered hope to Palestinians.

The US has been reaching out to leaders across the Middle East as Israel and Hamas trade volleys of fire.

Secretary of state Hillary Clinton has spoken to the foreign ministers if Israel, Turkey and Egypt in the past few days, as well as Jordan's King Abdullah.

But the US has been clear in pledging its support for Israel, its staunch ally.

Obama, who was on Saturday making his way to south-east Asia for a three day trip, has spoken to prime minister Binyamin Netanyahu every day since the current round of Israeli air strikes in Gaza commenced.

At a briefing on Friday, a State Department spokeswoman summed up the US position: "We are urging a de-escalation of this conflict. We are urging those countries with influence on Hamas and other groups in Gaza to use that influence to get a de-escalation," the spokeswoman said.

"We support … Israel's right to self-defence, and we obviously express our regret and sadness for the loss of life on all sides."

Israel has seen the US stance as a clear signal that it has a virtually free hand.

On Friday, the Israeli ambassador to Washington, Michael Oren, said during a visit to Capitol Hill: "The United States has given us the full backing to take whatever measures are necessary to defend our citizens from Hamas terror." Meanwhile, the Palestinian delegation to Washington has condemned the US response to the crisis as "biased and weak".

Despite diplomatic efforts, the violence continued on Saturday.

Israeli air strikes hit the office building of the Hamas prime minister in Gaza, amid warnings of a dangerous escalation in the conflict with up to 75,000 Israeli reservists mobilised for a possible ground invasion.

An explosion and air raid sirens were also heard over the Israeli port city of Tel Aviv as Palestinian militants in Gaza continued to fire rocket salvoes across the border four days after Israel launched an air offensive. So far Israel has struck more than 800 targets in Gaza while Gaza officials there said about 500 rockets had been launched so far at Israel.