WASHINGTON — FOR four years, American policy toward Syria has been built on a wish and a prayer: a wish that President Bashar al-Assad would leave and a prayer that the “moderate” Syrian opposition would be more than it is. Now Russia has stepped up its game, and the response from the American government and many commentators seems to be to wish harder and pray more, while condemning Russia for intruding where it supposedly doesn’t belong.

As much as many Americans and Europeans may abhor what President Vladimir V. Putin of Russia did in Crimea and Ukraine, Moscow’s intervention in Syria may offer the first glimmer of hope for ending the quagmire there. Mr. Putin is right that only stable governance and security will allow Syrian refugees to return home.

Rather than pursue decisive victory, America must seek to end this war with a less dramatic, less satisfying settlement.

The United States should have two goals in Syria. First, bring order to those parts of the country that the Islamic State does not control. Second, strive to build a coalition of forces that can contain the Islamic State and eventually replace it. Russia’s “intrusion” could offer a chance to achieve both.

This means setting aside American prejudices and heated political rhetoric. Russia isn’t an intruder in Syria; it has been involved there for decades, just as America has been involved throughout the Middle East for more than 60 years. Mr. Assad is Russia’s protégé, and Syria is an operations base for the Russian military. The United States has its own, significantly larger set of friends and operating facilities in the region.

At present, both powers have an interest in regional stability. Violent jihadist movements pose more of a threat to Russia than to America; many Russians have already died at the hands of terrorists, and thousands of Russian-based jihadists have flocked to the Islamic State with the intent to return home eventually.

Russia also has valuable leverage in Syria that America lacks: a military presence on the ground, a link with a weak but operating regime in Damascus, working ties with the Iranian and Iraqi governments, and an intelligence-sharing agreement with both that could well include Iranian allies like Hezbollah.

The United States still has hundreds of aircraft and thousands of troops in the area, as well as strong ties to the Kurds. But it has few links with Iran, a troubled relationship with the weak Iraqi government, very poor intelligence in Syria and a military training program for the moderate Syrian opposition that — recognized as a complete failure — has now been abandoned.

With proper safeguards and caution, a broader regional coalition could be a powerful tool against the Islamic State. American officials should acknowledge these realities and use the assets still available to them to advance their humanitarian and anti-extremist goals.

Russia must face reality as well. Mr. Putin will have to accept that Mr. Assad can’t remain in office in perpetuity and that his regime must change. The alternative is chaos, an opportunity for the Islamic State to embed itself and expand its operations, and an end to any role in Syria for Mr. Assad’s minority Alawite sect (an offshoot of Shiite Islam). A rump coastal state with Mr. Assad in charge, which may be Russia’s fallback option, wouldn’t remove the larger threat the Islamic State poses to Russia’s security.

There is a risk that Russia might overreach, as the United States did in Iraq and as both countries did in Afghanistan, if Mr. Putin imagines that outside military force alone can defeat the Islamic State. American hawks like Senators John McCain and Lindsey Graham make this same mistake. They’ve forgotten that opposing outside military interference is a critical ingredient of extremists’ recruitment efforts.