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In the first official military contact since the bombing began, Nato Supreme Commander General Wesley Clark and the Yugoslav chief of staff spoke by telephone late on Thursday night.
Officials say there will now be a meeting between its commanders and Yugoslav military officials on Saturday - but not in Belgrade - to discuss how to verify the troop withdrawal.
Nato says verification is a prerequisite for it to end its air campaign.
Nato spokesman Jamie Shea confirmed that the meeting will be led by British General Michael Jackson and would take take place somewhere on the border with Serbia.
German Chancellor Gerhard Schröder, speaking at the end of a two-day EU summit in Cologne, said: "We have reached a political breakthrough, peace is within reach and we are not going to let it slip through our fingers."
But he also insisted there would be no ceasefire until Serb forces withdrew from Kosovo.
The Reuters news agency reports EU sources as saying the bombing could end on Sunday.
US President Bill Clinton said he was anxious to end the bombing, but not until Yugoslav President Slobodan Milosevic complied with the peace plan.
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Yugoslavia's ambassador to Belgium has said his country has made gains from the peace deal agreed on Thursday.
Nikola Cicanovic told the BBC that Yugoslavia had gained better guarantees for its sovereignty and independence.
(Click here to see a map of Nato's overnight strikes)
Both Russia and China called for an immediate end to Nato strikes.
Experts from the Group of Eight (G8) countries - the G7 industrial nations plus Russia - have completed a draft UN resolution to be put to the United Nations Security Council.
The UK announced 4,000 British troops would leave at short notice for the Balkans.
The Clinton administration has also intensified planning for deploying international peacekeepers, returning refugees and reconstructing Yugoslavia.
But US officials said everything now depended on President Milosevic's next move.
Belgrade climbs down
The agreement passed by Belgrade provides for an end to the fighting in Kosovo, a rapid withdrawal of Serb forces, the deployment of a security force "with essential Nato participation", the safe and free return of the refugees and autonomy for Kosovo.
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Those conditions were originally rejected by the Serb delegation at two sets of talks in France in February and March of this year.
The announcement of a breakthrough came on Thursday after a second day of talks in Belgrade between Mr Milosevic, Mr Ahtisaari and Mr Chernomyrdin.
The Serbian parliament had earlier paved the way for Mr Milosevic's apparent climbdown by voting in a stormy session to accept the international peace plan presented by the two envoys.
Where now for Milosevic?
The agreement leaves Mr Milosevic facing an uncertain future. Washington has insisted that only the people of Yugoslavia can decide whether to remove him as president.
But American officials have said pointedly that the US will block international funding for Serbian reconstruction until Belgrade pursues democratic reform. They said Yugoslavia would not be welcomed as a full partner into the international community with Mr Milosevic still in charge.
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The deal was met with a sceptical response by the Kosovo Liberation Army (KLA). The plan requires the KLA to be "demilitarised", and does not deliver the organisation's goal of an independent Kosovo.
Spokesman Pleurat Sedjiu said commanders were still considering the proposals, but was doubtful they would accept it.
He told BBC television's Newsnight programme: "The first signs are not so positive. Milosevic will try through this to be sure that Kosovo will be part of Serbia forever."
Refugees are the losers
The UN refugee agency said it was now bracing itself for the task of supervising movement of almost two million refugees in the Balkans.
The former envoy to Yugoslavia, Lord Owen, said the deal was not a victory for Nato.
He said: "I don't think (the word) victory can possibly be used when we have over a million people pushed out of Kosovo, refugees sitting in terribly squalid conditions and a real worry that we won't be able to get them back before winter.
"I think we have got to face the fact that this has been a disaster and the worst case of ethnic cleansing since the Holocaust."
However, Foreign Secretary Robin Cook said: "It is a very significant breakthrough. The agreement which has been secured meets all our key objectives."
Bombardment continues
There were reports of overnight explosions in Kosovo, but there was no air raid alert in the capital Belgrade for only the second night since the bombardment began 72 days earlier.
Three detonations were reported near the Novo Brdo mine about 30km (20 miles) east of Pristina.
Nato planes also reportedly fired four missiles at a factory in Prizren.
Several explosions were heard in the Gora region in southern Kosovo and three bombs fell in the Leskovac region 280km (175 miles) south of Belgrade.
Four more bombs struck a television transmitter near Trgoviste, 300km (200 miles) south of the capital and several missiles hit near Kursumlija, near the administrative border with Kosovo
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(click here to return)
Q & A: Did the Serbs lose out?
(04 Jun 99 | Europe)
Serb media plays up sovereignty issue
(04 Jun 99 | Monitoring)
Refugees sceptical about peace
(04 Jun 99 | Europe)
Analysis: The limits of air power
(04 Jun 99 | Europe)
Milosevic 'must stand trial'
(04 Jun 99 | UK Politics)
Press review: Looking towards peace
(04 Jun 99 | Europe)
Refugees still wary of Serbia
(03 Jun 99 | UK)
Clinton's sigh of relief
(04 Jun 99 | Americas)
Full text of the peace document
(04 Jun 99 | Europe)
Backlash fears for Milosevic
(03 Jun 99 | Europe)
'Thousands of Serb troops killed'
(03 Jun 99 | Europe)
Tanjug's details of 'basis for peace'
(03 Jun 99 | Monitoring)
The problems now facing Nato
(03 Jun 99 | Europe)
Serbian Ministry of Information
Russian Ministry of Foreign Affairs
Kosovo Crisis Centre
Eyewitness accounts of the bombing
Nato
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