Russia’s recent intervention in Syria has ruffled feathers in Western capitals. On Tuesday came claims from NATO that Russia had moved ground troops into Syria, only a week after Russia launched its first airstrikes in the country. The moves prompted renewed calls from many in Washington — including former Secretary of State Hillary Clinton — for the Obama administration to impose a no-fly zone and begin arming the Syrian rebels in earnest.

President Obama should resist such clarion calls and refrain from escalating the conflict in such a manner. Indeed, he should be wary of much of the talk we are hearing about “doing more,” lest he risk exacerbating an already growing crisis.

Western powers were able to impose a no-fly zone in Libya in 2011 with ease, making it tempting to try to repeat the trick in Syria. But Libya was an unusually permissive environment for such action, and NATO aircraft faced virtually no resistance. That would surely not be the case in Syria. Indeed, now that Russian pilots are flying throughout western Syria, any attempt to impose a no-fly zone would present an unacceptable risk of direct hostilities between U.S. and Russian forces.

Moreover, a no-fly zone would offer limited benefits. It is typically easiest to restrict the operation of fixed-wing aircraft. For the past few years, however, Syrian President Bashar al-Assad’s forces have primarily used helicopters to deliver barrel bombs. A no-fly zone might therefore fail to counter what is actually the greatest threat to Syrian civilians.

Even if a no-fly zone were to succeed in grounding al-Assad’s helicopters, it would do little to arrest the fighting on the ground. In 2011, Obama authorized airstrikes against Moammar Gadhafi’s ground forces because he recognized that a no-fly zone alone would do little to prevent them from attacking rebel forces holed up in Benghazi. Although al-Assad’s ground forces have been seriously weakened, similar airstrikes would surely be necessary to forestall attacks against rebel forces.

That said, President Obama has evinced little inclination to impose a no-fly zone. What he does appear to be more susceptible to, though, are calls to arm the Syrian rebels. Last week, for example, he approved the direct provision of ammunition and arms to Syrian rebel forces.

Yet that decision is fraught with risks. The Obama administration appears inclined to draw a clear distinction between its campaign to degrade and destroy ISIS and the fight to topple al-Assad. Yet maintaining that distinction is untenable. If U.S.-armed rebels are able to eradicate the Islamic State, an unlikely scenario to say the least, they are likely to then turn their attention toward the al-Assad regime.

The reality is that even with the benefit of American arms, rebel forces are unlikely to be able to overcome Russian-backed regime forces. As during the Cold War, U.S. and Russian arms supplies will simply fan the flames of conflict and beget more death and destruction.

The most likely outcome of such a proxy war would be some sort of stalemate in which the al-Assad regime controlled most of Syria’s coastal region and the rebels controlled most of the territory to the east. Since the Syrian opposition is made up of a patchwork of rebel groups, with different ethnicities, beliefs and goals, such partition would be inherently unstable. In all likelihood, the various rebel forces would begin fighting amongst themselves.

That highlights one of the potentially fundamental flaws with arming the Syrian rebels. Although the provision of arms might increase their ability to combat ISIS (and al-Assad), it would do nothing to increase their capacity to construct effective governance structures in the territory under their control. More arms would simply increase the eventual need for the international community to deploy some kind of post-conflict stabilization force when it comes time to rebuild Syria.

Up to this point, President Obama has exercised commendable restraint in resisting pressure to “do more” in Syria. It would be folly to abandon that course in some sort of knee-jerk reaction to Russian intervention. Neither imposing a no-fly zone nor arming the Syrian rebels will contribute to the resolution of the war in Syria.

As the President has said repeatedly, there can be no military solution to the conflict. He should continue to heed his own advice.