Both Yugoslav leader Slobodan Milosevic and representatives of the Kosovo Liberation Army said they wanted to think over Nato's proposal for peace talks before responding.
Only the province's relatively powerless, moderate-Albanian leader, Ibrahim Rugova, who does not have forces involved in the civil war, promised to attend the talks.
"This is as good a result as we could have hoped for," said a Foreign Office source.
Mr Milosevic told Mr Cook that he was "committed to a peaceful solution" in Kosovo. But in a statement after the meeting he suggested that Serbia might refuse to take part in talks scheduled for Saturday at the Chateau of Rambouillet, near Paris. The problems of Kosovo, "an integral part of Serbia", should be settled "peacefully in Serbia," he said.
Adem Demaqi, who speaks for a wing of the KLA, and Rexhep Qosja, who represents the Albanian Democratic Movement, said they had taken very careful note and would give their response in a few days.
The six-member "contact group" has set a deadline of three weeks to reach an agreement. Nato ambassadors yesterday authorised air strikes against Serbia if necessary. If the KLA refuses to attend talks, it could face an arms blockade.
Bad weather disrupted Mr Cook's visit to Yugoslavia, and curbed the violence in Kosovo which brought him here.
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