The Nato air strikes on Bosnian Serb ammunition stores last week, though approved by the alliance as a whole, were to a large extent prompted by the US, anxious that the UN and Nato should not lose credibility in the Balkans. The UN's failure to respond to heavy Bosnian Serb shelling of Sarajevo three weeks ago fuelled American concern that the UN peacekeeping operation in Bosnia might be seen as so ineffective that it would have to be wound up.
However, Nato's first round of air strikes on Thursday drew a firm rebuke from the Russian foreign ministry, which called the action misconceived and one-sided. "This will not bring peace any closer, will only make it harder for UN troops to carry out their mandate, and will in the long run complicate efforts to find a political solution to the conflict," its statement said.
President Boris Yeltsin went even further after Friday's attacks, telling John Major and Chancellor Helmut Kohl of Germany that he was "seriously dissatisfied" that Nato had launched the strikes without consulting Russia.
For the moment, there has not been a complete split between the US and Russia. The two countries remain connected through the "contact group'', which is trying to broker a Bosnian peace and which also includes Britain, France and Germany.
But contact-group unity is not all it should be. No sooner had a US envoy, Robert Frasure, flown home from Belgrade after failing to persuade President Slobodan Milosevic of Serbia to recognise Bosnia in its pre- war borders than a Russian official, Alexander Zotov, arrived with a different, and more conciliatory set of proposals.
Still, the Russian leadership has no great love for the Bosnian Serbs, and Mr Yeltsin and his colleagues are far less sentimental about their fellow Orthodox Slavs than is sometimes supposed in the West. They are incensed at the fact that Bosnian Serb forces have intimidated Russian soldiers in the UN contingent as much as those from other countries.
None the less, there are clear limits to what Russia will tolerate in terms of Western military action in the Balkans. Rather as Churchill and Stalin once made an informal deal to treat Yugoslavia as a country where the West and Russia would have an equal degree of influence, so present-day Russian leaders reject what they view as a Western attempt to dictate a Balkan settlement through the use of force.
There can be little doubt that, if Nato were to raise the stakes by increasing its air attacks, Russia would take a much less cooperative attitude towards the West on a whole range of international issues. From a European point of view, the most important is the attempt by the European Union and Nato to bring new democracies such as the Czech Republic, Hungary and Poland into the Western economic and security camp.
The West points out that Russia has no veto on central and eastern European membership of these institutions, but the Kremlin can show its anger in many ways, above all by refusing to co-operate in pan-European security affairs. For some time Moscow has been looking for a reason to revise the Conventional Forces in Europe treaty, which it says unfairly restricts Russian troop levels.
As far as Bosnia is concerned, the US and Russia can probably avoid confrontation as long as the UN peacekeeping operation remains in place and the US takes no active steps to arm the Muslims. But if the UN were to leave Bosnia - and France's new leaders under President Jacques Chirac have notified the UN that French troops will start leaving from late July - then the picture would begin to darken.
It would darken even more if Senator Robert Dole were to succeed in his effort to pass legislation next month to lift the arms embargo against the Bosnian government. The practical importance of this step might be limited, in that the Bosnian forces are clearly already receiving weapons from abroad in violation of the embargo, but such a decisive US alignment with the Muslim cause would surely provoke a matching response from Russia with regard to the Serbs.
The crucial factor is whether the UN can stay in Bosnia. Last week's American-led air strikes were intended to shore up the UN operation by showing that it was not as feeble as it has often looked. But arguably the air raids will ultimately serve to undermine the UN because, in the end, neither Nato nor the UN forces have the will or the mandate to defeat the tenacious and ruthless Bosnian Serbs.
The truth is that for more than two years the West has not had any satisfactory options in Bosnia. It cannot fight a full-scale war against the Bosnian Serbs, but it cannot afford to let the Muslims go under. It cannot pull out the UN forces, but it cannot let them stay in intolerable conditions. The choices are appallingly difficult and, whatever is decided, there is no guarantee that it will lead to peace.