WASHINGTON — The Obama administration is locked in a sharp new debate over whether to deploy American 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 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 Ashton B. 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 Mr. 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.