WASHINGTON (Reuters) - Already out-gunned and out-manned in Syria’s civil war, U.S.-backed rebels are facing a new and possibly even more serious threat to their survival: Russian air strikes that Washington appears reluctant to thwart.

The Obama administration – blindsided by the speed of Moscow’s direct intervention and a Russian target list that included CIA-trained fighters – made clear on Thursday that the it had no desire to increase the risk of an air clash between the former Cold War foes.

While Washington took pains to insist it still considered the “moderate” opposition vital to Syria’s future and was not abandoning them, withholding U.S. air cover could further jeopardize beleaguered rebel forces.

President Barack Obama has rarely launched military action in support of the opposition in four years of Syria’s civil war and is hesitant to get further ensnared in the conflict. Even if he wanted to, he could face legal limitations due to the scope of his presidential war powers.

The rebels have already struggled in the fight against the Syrian military, dogged by internal divisions and the rise of radical jihadist groups such as Islamic State and the al Qaeda-linked Nusra Front.

Russian warplanes, in a second day of strikes on Thursday, bombed a camp run by anti-government rebels trained by the CIA, the group’s commander said, even as Russia insisted it was hitting only Islamic State forces, a common enemy of Washington and Moscow. U.S. officials believe Moscow’s main objective is to prop up its ally, Syrian President Bashar al-Assad.

Russia’s deepening role, together with inconclusive talks between the U.S. and Russian militaries on air safety on Thursday, underscored the consensus in Washington that Obama has few good options for turning the situation around.

Obama does have the power to expand the arming of moderate rebels so they can better defend themselves or to set up no-fly zones, as some critics at home have demanded, but U.S. officials note that such measures would carry their own risks of escalating Washington’s involvement.

Russian President Vladimir Putin appears to be betting that Obama, wary of seeing the United States pulled into another Middle East war, would be unlikely to respond aggressively.

“Mr. Putin reads the Obama administration well,” wrote Aaron David Miller, a former Middle East adviser to Democratic and Republican administrations. “He knows that President Barack Obama never wanted to militarize the U.S. role in Syria.”

Further complicating the U.S. response, Lebanese sources said hundreds of Iranian troops have arrived in Syria to join a major ground offensive in support of Assad.

“BURDEN ON RUSSIA”

The CIA has run an ostensibly covert training program for vetted Syrian rebel groups deemed moderate by Western states that have supported the uprising against Assad. The plan is separate from the U.S. military’s train-and-equip program aimed at building a Syrian rebel force to fight radical Islamic State insurgents. That program is considered to have all but failed.

White House spokesman Josh Earnest blasted Russia for “indiscriminate bombing of Syrian opposition targets” and said it was making a “grave miscalculation”.

But when asked whether the United States would do anything to protect them from Russian air strikes, he told reporters: “I think the burden here is on Russia.”

Earnest did not rule out the possibility that Russia, already under U.S. sanctions over the Ukraine crisis, could face diplomatic consequences over its actions in Syria, though he suggested that Moscow would suffer more if it is “sucked into a years-long sectarian conflict” there.

The message from the Obama administration, whose efforts to train and equip moderate insurgents have moved slowly and often ineffectively, appeared to be that they must fend for themselves for now in the face of Russian air strikes.

Even if Obama was willing to risk seeing a proxy conflict in Syria escalate into direct U.S.-Russia confrontation, he seems to be hemmed in by his own rules of engagement there.

The letters that Obama has sent to Congress invoking his war powers since launching the anti-Islamic State campaign last September have stated that he is limiting it to “air strikes and other necessary actions against these terrorists” in Syria as well as Iraq.

U.S. officials have not ruled out that rebel forces could receive air cover if attacked by Assad’s air force. But so far that is not believed to have happened.

One U.S. official, speaking on condition of anonymity, said the Obama administration was reviewing the legal implications of Russia’s direct involvement in Syria’s conflict.

At the Pentagon, spokesman Peter Cook repeatedly declined to discuss whether the United States might be called upon to defend moderate Syrian rebels under Russian attack, calling it “hypothetical.”

Senior U.S. military officials raised American concerns about Russia’s choice of targets in a secure video call on Thursday with Russia counterparts.

The call, which the Pentagon described as cordial and which lasted just over an hour, focused on ways to safely keep U.S. and Russian jets apart as the two militaries carry out parallel campaigns with competing objectives. Washington also wants Russia to agree to stop striking moderate rebel targets.

U.S. Senator John McCain, a Republican who leads the Senate’s top military committee and is a frequent critic of Obama’s foreign policy, questioned the logic of such coordination, which in military parlance is known as “deconfliction.”

“Are we trying to ‘deconflict’ with Russian air operations that target U.S.-trained rebels?” McCain asked.