The appointment of Viktor Chernomyrdin suggests that Mr Yeltsin is moving beyond explosive denunciations of the Nato air strikes - such as his infamous "Third World War" warning - towards securing a position for Russia as mediator.
Although the majority of Russian politicians have condemned Nato, Mr Chernomyrdin has been less vocal than most. As prime minister from 1992 to 1998, he acquired a reputation as a compromiser who leans considerably more to the West than the current Prime Minister, Yevgeny Primakov, or his government.
Moscow knows the Kosovo war could provide it with a golden opportunity to play a starring diplomatic role, its best chance to do so since the break-up of the Soviet Union. It also knows this means ignoring domestic pressure to give unqualified support to the Serbs. Mr Yeltsin - if not his administration, with whom he has strained relations - appears to be trying to grasp that opportunity.
Russia should take the chance to end the bloodshed now, "when there are neither winners nor losers", Mr Chernomyrdin said yesterday. Moscow would step up its diplomatic efforts "in all directions" to bring an end to Nato bombing. But, in an unusually even-handed remark by Russian standards, he said that both "belligerent parties" should be brought to the negotiating table.
Although the 61-year-old is derided as a fat-cat windbag by many Russians who resent his role in the failed market reforms, he has the advantage of good connections. He is personally acquainted with the two biggest players, Slobodan Milosevic and Bill Clinton, whom he plans to visit soon.
Mr Chernomyrdin is generally approved of by Western leaders, who see him as a member of the exiled team of market reformers who once dominated the Russian government. The Kremlin was keen yesterday to advertise his "great political experience", and "broad international recognition".
Mr Yeltsin's move comes amid a general toning down of Russia's expressions of outrage over the Yugoslav war, after an initial burst of fury. The most striking example of its new strategy came during Tuesday's meeting in Oslo between Madeleine Albright, the US Secretary of State, and her Russian counterpart, Igor Ivanov. Although their talks brought little concrete progress, both sides vowed to continue talking and there was a largely co-operative mood - a far cry from the previous week.
In recent days, Russian television coverage of the Balkans has become more balanced, and now includes accounts of the suffering of the refugees.
News of the Yugoslav parliament's vote to join the Russia-Belarus union was greeted coolly in Moscow; public opinion surveys showed that more than two-thirds of Russians were not interested in joining a political embrace with their troubled Slavic cousins.
The fact that 20 per cent of the Russian population is Muslim has finally begun to filter through to the ivory towers. Combine that with the country's need for Western loans and investment, and it becomes clear that Russia could not sensibly give unqualified support to Mr Milosevic, even if it wanted to.