This week, unexpectedly, Syrian President Bashar Assad turned up in Moscow. He hasn't been seen outside Syria since unrest broke out four years ago.

The trip makes two important statements.

The first is that, thanks to Russian air strikes, the Syrian state — the actual Syrian state recognised under international law — is breathing again. Assad holed up in Damascus looked like a Ghaddafi waiting to happen. Assad in the Kremlin looks like the head of a country with a seat at the UN.

The second is that Moscow wants a political solution to the Syrian crisis. Many rushed to interpret Assad's Moscow cameo as a calculated Russian show of defiance. But the Russian President used the few words he gave journalists to repeat Russia's commitment to a political compromise ('a long-term settlement based on a political process that involves all political forces, ethnic and religious groups'), one which Putin hoped could be achieved 'in close contact with the other global powers and with the countries in the region' — above all, the US and its Middle Eastern allies, but also Europe.

It was a reiteration of the messages Moscow has been sending for weeks.

No good reason exists to treat this as smoke and mirrors. Russia doesn't actually want to dictate unilaterally how this mess ends — it doesn't possess the resources for that. But it does want to ensure that the outcome of Syria's civil war respects a principle of legitimacy it has taken as a national cause and, secondly, protects Russia's wider interests in the Middle East.

Will the US play ball?

US Foreign Secretary John Kerry is meeting Russian Foreign Minister Sergei Lavrov in Geneva today. All the same, it seems improbable that the US will cooperate openly with Russia in Syria, and certainly not in a way that suggests US support for Assad.

But Russia isn't primarily asking the US and other Western countries flying missions over Syria (illegally, as Moscow enjoys pointing out) to join with it in a grand coalition against terrorism. Such proposals really belong more to the theatrics of international diplomacy than its substance. Rather, Putin is inviting the US to negotiate. Moscow wants to harness US diplomatic influence to create the conditions for a comprehensive political compromise, one Washington's major allies in the region can support.

For Russia, any deal must include the present Syrian state (perhaps over only part of its present area and possibly without Assad, though he will have to remain symbolically at the helm for a while), and the security of Russia's Mediterranean bases.

Can Moscow persuade Washington there's enough in it to justify US involvement?

Henry Kissinger has recently reminded us that the US designed the post-1973 Middle Eastern order precisely to keep other powers out, and as far from the Persian Gulf as possible. Russia's intervention in concert with Iran on Assad's behalf heralds the failure of that strategy. Kissinger doesn't go this far, but it's hard to escape the conclusion that Washington's own policies have helped sow the chaos that has prompted Russia's intervention. Since its 2003 invasion of Iraq, the US has been the region's real revolutionary power.

One way, therefore, of looking at Moscow's appeals for a deal on Syria is as an opportunity for Washington to put a lid for a while on the region's destabilising conflicts, and to support the cause of order rather than revolution (as its interests have already led it to do in Egypt and Bahrain) in the hope that a return to stability will create the kind of conditions in which an orderly evolution towards more liberal regimes will become possible. It's a solution so thoroughly in the spirit of Vienna in 1814 that's it's hard to imagine Kissinger not being intuitively disposed to it.

Indeed, he recognises Moscow's intervention as a classic balance-of-power maneuver: 'It is a geopolitical, not an ideological, challenge', he writes, 'and should be dealt with on that level'. But he adds that between Russia and the US 'there exist compatible objectives'.

In persuading the US to see the situation as such an opportunity, Turkey is especially important. It's a longstanding US ally and opposes Assad, but equally cannot reconcile itself to Washington's pro-Kurdish policies, whether in Syria or neighbouring Iraq. Turkey has also been a friend to Russia on Ukraine-related sanctions. If Russia can secure Ankara's support for a political solution (there are rumours Ankara could tolerate the presence of Assad for up to six months as part of a negotiated plan), Washington will come under great pressure to find a way of creating the diplomatic conditions for one. The Turks, with the Saudis, will take part in today's meeting between Kerry and Lavrov in Geneva.

It's conventional to think of wars creating political realities, but skillful diplomacy has turned these realities around, to the disadvantage of the ostensibly stronger power. But although Moscow has saved Assad's 'legitimate' state, it cannot legitimise a new Syria or a new regional order alone. If the US wants Assad gone, the quickest way of achieving this is to make Assad's departure its price for working with Moscow.

Washington shouldn't expect Moscow to sacrifice the kernel of the Syrian state it has saved. But it should take seriously its call to talk. If the Russian jets flying above the Syrian desert confirm anything at all, it's that even in the prized Middle East, the US unipolar moment is over.