Mr Hill, who had talks in Pristina with the moderate Albanian leader, Ibrahim Rugova, a day after handing the latest peace blueprint to Serbia's President Milan Milutinovic, said the plan was "still a draft, but ... one that is getting into increasingly final form." Wide autonomy is proposed for Kosovo, to secure a permanent settlement in the region.
On Friday General Wesley Clark, Nato's supreme commander, warned at an alliance meeting in Edinburgh that if no political solution were found, serious fighting could resume in two to four months: "Both the Kosovo Liberation Army and the Serbs are rearming and preparing for confrontation again. We must use this respite to achieve a just and durable political settlement."
Mr Hill, speaking a day after a Yugoslav army soldier was killed and four wounded in an ambush on an army convoy in Kosovo, said: "We are very worried about continuing infractions of the ceasefire. If people have suggestions for [a political solution], they better get them to us quickly ... Things are going to happen very quickly in the coming weeks."
Time is vital on humanitarian as well as political grounds: for the more than 250,000 ethnic Albanians who fled their homes during this year's fighting, renewed unrest would impede their return, and leave many exposed to winter as well as war.
The latest violence coincides with the arrival of 2,000 unarmed monitors from the Organisation for Security and Co-operation in Europe. Their goal is to ensure that President Slobodan Milosevic of Yugoslavia is keeping his side of the deal.