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Before meeting the US and EU envoys, Strobe Talbott and Martti Ahtisaari of Finland, Mr Chernomyrdin expressed optimism that a diplomatic breakthrough was on the horizon.
"This week must be decisive in the search for a compromise on how to direct the military conflict into a political channel," he said.
"All sides, including the United States, Europe and Russia have an enormous desire to find a political solution."
On Wednesday, Mr Chernomyrdin is expected to go onto Belgrade for the fifth time since the crisis began.
His optimism has also been echoed by Germany and France.
The German foreign minister said current diplomatic efforts are covering new ground, while his French counterpart also predicted that a decisive moment is approaching.
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The new signs of optimism come after the Yugoslav authorities repeated their willingness to abide by the principles set out by the G8 countries for an end to the conflict.
However, the BBC Moscow Correspondent Paul Anderson says Mr Chernomyrdin has made similar predictions on previous occasions, which came to nothing.
And there is still no indication that Belgrade would allow a Nato-led peace-keeping force to enter Kosovo.
But Nato military commanders are nevertheless meeting in Brussels to determine how to bring the number of troops in such a force up to 50,000.
Nato bombs Albania
Despite the political negotiations, intensive strikes continued with reports that Nato bombing has strayed into Albania, near the country's border with Kosovo.
The BBC's Jeremy Cooke says the strikes are heavy, with several waves of aircraft dropping laser-guided bombs.
Earlier, the border area had been subjected to three days of heavy Serbian shelling after attempts by the KLA to open a supply route along the border.
There are also reports that Nato has caused civilian casualties in three separate incidents in the past two days.
Nato has admitted that a bomb went astray during an attack on an army barracks in the southwest Serbian town of Novi Pazar.
Yugoslave media said at least 11 people were killed and 23 injured when Nato missiles hit an apartment building in the town.
(Click here to see a map of latest Nato strikes)
Nato spokesman Jamie Shea said that five out of six weapons hit the army barracks, but that one went astray, overshooting the target by about 60 metres, and may have hit residential buildings.
He said Nato could not confirm any civilian casualties but regretted any unintended damage.
The Yugoslav state news agency Tanjug said Nato's targets included a publishing house, printing presses and regional television and radio headquarters close to a hospital and a bus station.
Nato is already investigating claims that at least 30 civilians had been killed in two other attacks in the previous 24 hours.
President Milosevic has attacked such actions, saying they could damage the peace process.
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(01 Jun 99 | UK)
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