WASHINGTON >> The Obama administration is locked in a sharp new debate over whether to deploy U.S. military forces to establish no-fly zones and safe havens in Syria to protect civilians caught in its grinding civil war.

The White House remains deeply skeptical about the idea, but the growing refugee crisis in Europe and Russia’s military intervention in Syria have increased pressure on President Barack Obama to take more forceful action. Secretary of State John Kerry and others renewed their push at a tense White House meeting on Monday to use air power to shield Syrians from the fighting, officials said.

But at the same meeting, which included Defense Secretary Ash Carter, a Pentagon report presented sobering estimates of the extensive military resources required to enforce such zones, leaving many at the table dubious about the wisdom of taking action. Russia’s own military operations in Syria raise the risk of an inadvertent clash if Americans try to block off certain parts of the country.

Nonetheless, the fact that the administration is even revisiting an idea it has previously rejected — just weeks after Obama publicly dismissed it again — underscored the urgency of the crisis as tens of thousands of Syrians flood Europe to escape the war zone and Russian airstrikes fuel the multisided conflict. It also suggested a frustration on the part of policy makers seeking a strategy that can succeed.

Among the options discussed Monday were establishing safe zones for civilians on Syria’s borders with Turkey and Jordan. Officials presented different variants, including some that had safe zones exclusively for humanitarian relief and more ambitious versions that would provide sanctuary for Syrian opposition forces allied with Americans.

But the Pentagon presentation laid out how many aircraft and personnel would be required, making it clear that there would have to be a significant escalation of U.S. air power in the region, according to officials who described private deliberations on the condition of anonymity. The officials said that the escalation would require aircraft and personnel beyond those already conducting airstrikes against the Islamic State in Syria and Iraq.

Obama did not attend the meeting, which was led by his national security adviser, Susan E. Rice, and no formal decision was made. But advocates of a greater American role left discouraged.

Some said they suspected that Pentagon officials, who have been resistant to further U.S. military intervention in Syria, inflated the figures to persuade the president not to change his policy.

Skeptics of intervention saw no indications that Obama would reverse himself, viewing the process as mainly an exercise in due diligence.

The White House declined to comment Thursday. But Obama has consistently rejected the notion of a no-fly zone, seeing it as a simple bumper-sticker idea with more drawbacks than benefits. Three weeks ago, he dismissed critics who have advanced what he called "half-baked ideas" that amounted to "a bunch of mumbo jumbo." And his spokesman, Josh Earnest, said that so many logistical questions surround a no-fly zone that it was "not something that we’re considering right now."

But the calls for action have only grown, including from veterans of the Obama administration. Former Secretary of State Hillary Rodham Clinton, now running for president, called this month for a no-fly zone "to try to stop the carnage." Two weeks ago former Defense Secretary Robert M. Gates wrote an op-ed article in The Washington Post with former Secretary of State Condoleezza Rice urging the president to rethink his opposition.

"No-fly zones and safe harbors for populations are not ‘half-baked’ ideas," Gates and Rice wrote. "They worked before (protecting the Kurds for 12 years under Saddam Hussein’s reign of terror) and warrant serious consideration." Gates, a defense secretary under President George W. Bush, was Obama’s defense secretary and a trusted adviser in his first term.

At Monday’s meeting, officials debated how the zones could be set up solely to protect civilians, rather than as staging areas for rebels to launch attacks against Syrian government forces.

Military experts cautioned that this would be difficult to enforce without large numbers of ground troops, most likely from Turkey or Jordan, in Syria.

"You need to be able to police the zones to keep the rebels out, because they have a natural incentive to move into the zones," said Karl P. Mueller, a policy analyst at the RAND Corp. and an expert in the use of air power.

Kerry and other advisers have for years argued for a more forceful U.S. role to stem the humanitarian crisis in Syria, while the Pentagon has voiced caution.

In a 2013 letter to Congress, Gen. Martin E. Dempsey, then the chairman of the Joint Chiefs of Staff, said any military intervention in Syria would be an "act of war." He estimated that establishing safe zones in Syria could cost more than $1 billion per month if U.S. ground troops were used — even stationed outside Syria — to assist regional forces patrolling the zones.

Dempsey’s letter also signaled his skepticism about either humanitarian zones or a no-fly zone across all of Syria.

"As we weigh our options, we should be able to conclude with some confidence that the use of force will move us toward the intended outcome," he wrote. "We must also understand risk — not just to our forces, but to our global responsibilities."

Russia’s increasing presence in Syria complicates the picture. Some former advisers to Obama said he missed his opportunity to impose a no-fly zone last summer before Moscow sent forces to bolster the government of President Bashar Assad. Doing so now would raise the question of how American pilots should respond if Russian aircraft disregarded the lines drawn by the United States and entered the no-fly zones.

The United States and Russia have just signed an agreement on how to avoid accidental encounters in the skies over Syria as they conduct separate operations. But there is no guarantee that the Kremlin would respect no-fly zones declared by the United States.

"To the extent that the Russians became concerned that the American intervention became a threat to the survival of the regime, they have the capability to deploy newer and more capable air defenses to Syria," Mueller said.

But Gates argued this week that Russia would defer to an assertive U.S. approach. "We should decide what we want to do in Syria, whether it’s a safe haven or anything else, and basically say, just tell the Russians, ‘This is what we’re going to do and stay out of the way,’" he told a Senate committee.

"And if it’s a safe haven and it’s in an area that doesn’t threaten Assad’s hold on power," he added, "then it seems to me that the chances of them challenging us are significantly reduced."