Viktor Chernomyrdin was expected to advise the Yugoslav President to accept a mixed international peace-keeping force in the province, containing Serbs and troops from Nato countries, the Russian media reported.
The idea is to meet both sides' main sticking points - Nato's demand for allied troops to be at the core of any peace force in Kosovo, and Belgrade's insistence on Serbia retaining a military presence in an area it sees as the cradle of its culture.
The Kremlin envisages Nato troops escorting the 800,000 Albanian refugees home while Serbs would retain control of ethnic Serb areas and holy sites.
Mr Chernomyrdin has threatened to pull out of the mediation drive altogether if Russia's plans are ignored and yesterday's trip could be the last throw of the dice.
The chances of success look poor, however.
Mr Milosevic has insisted that any peace force in Kosovo must be lightly armed and may not include Nato nations. He fears Western troops will try to arrest him, and his worries on that score will have been increased by his indictment on Wednesday as a war criminal by the Hague-based International War Crimes Tribunal for former Yugoslavia.
Nor does Nato look ready to compromise. Pouring water on the Russian peace initiative even before it began, the US deputy secretary of state, Strobe Talbott, yesterday insisted that Russia's mediation effort was purely Russia's affair and had no bearing on what the West was trying to achieve.
"Serbs carrying guns have been so dramatically and atrociously part of the problem in Kosovo that it is simply nonsense to think they could be part of the solution," Mr Talbott said, knocking down one of the main planks of the Kremlin's peace proposal.
At the same time, the head of the rebel Kosovo Liberation Army, which Mr Chernomyrdin calls a terrorist organisation, was due to pay a visit to Nato headquarters yesterday.
Nato stressed that Hashim Thaci's visit was "informal" and that he would not be meeting the secretary-general of Nato, Javier Solana. But it could only be seen as a sign of growing co-ordination between the Kosovo guerrillas and the alliance.
Russia is loath to see the KLA play any role whatsoever in a Balkan peace settlement and says it must be disarmed. Instead, nine weeks of Nato bombing have helped the KLA to grow in size, US defence experts said.
The top intelligence officer for the US joint chiefs of staff, Rear-Admiral Thomas Wilson, said the KLA has tripled in size - from about 5,000 troops in March to at least 15,000 now.
The KLA is still smaller than the 40,000-member Serb army and police troops in Kosovo, but it is effective at attacking Serb forces essentially pinned down by the Nato bombing, Rear- Admiral Wilson said.
Thursday's raids were the heaviest yet, with 800 sorties, and knocked out Belgrade's electricity supply.
Nato chiefs said yesterday that as the number of sorties was expected to rise, the alliance would soon be in a position to carry out 24-hour bombing. It said forecasts of more clear weather in the days ahead would enable it to step up attacks still further against Serb forces in Kosovo.Reuse content