WASHINGTON, June 1 (Andrew Quinn/Reuters) - US Secretary of State Hillary Clinton on Tuesday called for careful responses to Israel's attack on a Gaza-bound flotilla, ignoring Turkey's demands for outright condemnation of the deadly assault.

Clinton, speaking amid a crisis that has poisoned ties between two close US allies and could imperil moves to relaunch the Middle East peace process, indicated the United States would not quickly join the international outcry against Israel over Monday's attack.

US President Barack Obama spoke by telephone with Turkey's prime minister, Tayyip Erdogan, to express his condolences over the loss of life in the Israeli raid and said the United States was working with Israel to secure the release of activists who had been aboard the flotilla of ships.

Clinton earlier met Turkish Foreign Minister Ahmet Davutoglu, who had demanded Washington take a clear stand against Israeli actions, which saw at least nine pro-Palestinians activists killed, most of them Turks.

I think the situation from our perspective is very difficult and requires careful, thoughtful responses from all concerned, she said after the meeting.

We support an Israeli investigation that meets those criteria. We are open to different ways of ensuring a credible investigation including international participation, Clinton said, without elaborating.

State Department spokesman P.J. Crowley said the United States would push for an international role in the probe.

Turkey has a vital interest in this. Other countries have a vital interest in this, he told a news briefing.

We will work, within the (Security) Council and more broadly, to see how an international element can be introduced into this investigation.

Davutoglu earlier told reporters that Turkey -- an important US ally on issues ranging from Middle East peace to the war in Afghanistan -- was disappointed that the United States had not offered stronger backing.

Some of our allies are not ready to condemn the Israeli actions, Davutoglu said, comparing the incident to the Sept. 11, 2001, attacks on the United States.

We expect full solidarity with us, he said. It should not be a choice between Turkey and Israel. It should be a choice between right and wrong.

International fury over the flotilla attack has created a tough balancing act for the Obama administration, particularly with Turkey, a key NATO ally seen by Washington as a secular Muslim power that can counter Islamic militancy in the region.

A senior administration official, speaking on background, said the United States saw mistakes on both sides.

We believe that there was a good-faith effort to provide humanitarian assistance to the people of Gaza. By the same token the organizers of the flotilla were clearly seeking a confrontation -- and tragically they got one, he said.

UNSUSTAINABLE AND UNACCEPTABLE

Without laying direct blame, Clinton said the flotilla incident underscored the unsustainable and unacceptable situation in the Gaza Strip, which been subject to an Israeli blockade since the Palestinian Islamist movement Hamas seized control of the coastal desert territory in 2007.

Israel's legitimate security needs must be met, just as the Palestinians' legitimate needs for sustained humanitarian assistance and regular access to reconstruction materials must also be assured, Clinton said.

She said the United States would continue to push to reunify Gaza and the West Bank under the Palestinian Authority through a two state solution negotiated with Israel.

This incident underscores the urgency of reaching this goal and we remain committed to working with both sides to move forward these negotiations, she said.

US Middle East peace negotiator George Mitchell was headed back to the region on Tuesday, hoping to press forward with indirect peace talks between Israel and the Palestinian Authority. White House spokesman Robert Gibbs said the administration expected the talks to go ahead despite the flotilla incident.

Getting the two sides to revive negotiations in April after an 18-month break was the Obama administration's most tangible Middle East achievement. But expectations remain low for a breakthrough and the flotilla crisis could complicate matters.

Davutoglu said Turkey would put on hold any moves to mediate restarting indirect Israeli-Syrian peace talks, which Washington sees as another crucial piece of the puzzle.

The United States and Turkey already were at odds over Iran, with Turkey and Brazil pushing a new proposed atomic fuel deal for Tehran as a diplomatic alternative to the tough UN sanctions that Washington wants.

The United States has rejected the proposal as too little, too late and says the measure does not address core concerns that Tehran is seeking to develop nuclear weapons. Tehran says its nuclear program is purely peaceful.

Davutoglu said on Tuesday the proposed fuel deal would be a confidence-building measure and rejected suggestions Turkey and Brazil were helping Tehran to delay UN action on sanctions.

This is not defending Iran, he said. This is defending regional peace, global peace and the national interests of Turkey.

(Additional reporting by Ross Colvin, editing by Bill Trott and Cynthia Osterman)