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.

America and Russia must accept that as outsiders, they will never be able to confront, contain and eliminate the Islamic State alone. Only a regional coalition could do so.

Working together, Washington and Moscow could take advantage of their respective ties with the regional powers that actually have the manpower and operating space to act: Turkey, Saudi Arabia, Iran, Iraq, the Gulf states and the Kurds. While any coalition would have internal tensions — most notably between Turkey and the Kurds — combined Russian and American pressure could help convince all parties to focus on the Islamic State today and leave other concerns for later.

To be sure, Russia’s main aim at the moment is bolstering Mr. Assad by attacking various anti-regime forces and leaving others to deal with the Islamic State. But groups like the Nusra Front — Al Qaeda’s affiliate in Syria — are not America’s friends either, and there is potential for an effective division of labor. Coordinating our actions could ensure that Russia does not focus on the groups America supports and could prevent the dangerous accidents that tend to arise in the fog of war.

A joint Russian-American effort may fail to solve the Syrian problem. It’s not a perfect remedy, but the partial overlap in American and Russian interests is the most promising route toward a solution. American officials must end their table-thumping about Russian intrusion, recognize that we are past the Cold War, and get down to the business of statecraft.