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But she was most circumspect about the Serbian side. Earlier she had told the Serbs to make concessions or face the risk of Nato air strikes.
Ms Albright issued the warning in an hour-long meeting with the Serbian President Milan Milutinovic in Paris.
Serbian sources said the meeting with Mr Milutinovic was tense and uncomfortable.
The British and French Foreign Ministers, Robin Cook and Hubert Vedrine, are also attending the talks at the chateau in Rambouillet, near Paris.
The rival Serb and ethnic Albanian delegations have spent the last week at the chateau embroiled in talks.
Both sides were forced to the table under the threat of Nato air strikes on Serbia and tough measures to cut off arms and financing for the separatist ethnic Albanian Kosovo Liberation Army (KLA).
More talks likely
The six-nation Contact Group is convening later to determine whether the two sides have made sufficient headway for talks to be allowed to continue for a further week.
BBC correspondent Jim Fish , who is at the talks, says the mediators are finding it difficult to establish who is making the decisions on both the Serb and ethnic Albanian sides.
Despite current slow progress, the international group of foreign ministers is widely expected to give the go-ahead for further negotiations.
Foreign ministers from the 15 European Union countries are also meeting in the French capital to be briefed on the talks, underlining the importance the West attaches to ending the 11-month-old conflict in which 2,000 people have died.
The peace blueprint would give Kosovo's ethnic Albanian majority substantial autonomy for an interim three-year period, while leaving the province within Yugoslavia. Serbian security forces would withdraw and the rebel KLA would be disarmed.
US backing
While Nato has threatened air strikes if the talks fail, it has also pledged a 30,000-strong ground force to police a peace deal.
US President Bill Clinton has given his backing to the plan, promising to send 4,000 troops to Kosovo. The UK has already pledged a substantial involvement - though numbers of troops have yet to be confirmed.
![[ image: width=150]](/olmedia/275000/images/_279277_albanian_demo.jpg)
Despite pressure to tackle differences, the Contact Group has problems of its own to resolve.
One member, Russia, has warned the West not to make the peacekeeping force an explicitly Nato operation.
Outside the talks venue on Saturday, riot police were deployed to control thousands of pro-Albanian demonstrators.
Many of them carried the red Albanian flag and banners in support of the rebel KLA. There were no reports of any violence.
Violence continues in Kosovo
The need for a deal was underlined by reports from Kosovo which said at least nine people were injured in a bomb explosion in the central town of Urosevac.
International peace verifiers investigating the blast said there was no word on who was responsible.
Correspondents say bombings have become increasingly frequent in the province with Serb or ethnic Albanian cafes often being the target.
Clinton approves US troops for Kosovo
(13 Feb 99 | Europe)
Kosovo talks: Half-way to a deal?
(13 Feb 99 | Kosovo)
Analysis: Selling a Kosovo deal to Russia
(13 Feb 99 | Europe)
Nato 'losing patience' with Serbs
(12 Feb 99 | Europe)
Thousands bury Racak dead
(11 Feb 99 | Europe)
Serbs attacked over peace delays
(12 Feb 99 | Europe)
UK troops on Kosovo stand-by
(11 Feb 99 | UK Politics)
Kosovo talks: The negotiators
(06 Feb 99 | Europe)
Serbia's Ministry of Information
US Senate Republican Committee - Kosovo
French Ministry of Foreign Affairs - Meeting on Kosovo
Kosovo Information Centre
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