The pair, who are co-chairing the talks, aim to throw their personal weight behind a process that is showing ominous signs of settling into diplomatic trench warfare.
Last night, after a second full day of talks behind closed doors at the former royal chateau at Rambouillet, there was no sign of a breakthrough.
The Serbs and the ethnic Albanians were re-iterating old demands: Belgrade wants a public statement by the Kosovo Albanians that Yugoslavia's borders will not change; the latter seek a formal ceasefire.
Both requests have crucial importance. A pledge of unchanged borders would amount to recognition that the Serbian province will not become independent. A ceasefire would constitute acknowledgement by the Serbs of the separatist Kosovo Liberation Army.
As these positions were set out once more, word came of five more killings in separate parts of the troubled province which is populated mainly by ethnic Albanians. Details of the attacks were sketchy, but the suspicion was strong that the bloodshed - like a bomb which killed three people in Kosovo's capital, Pristina, on Saturday - was aimed at derailing the Rambouillet talks.
British diplomats insisted that the decision by Mr Cook and Mr Vedrine to go back to Rambouillet did not signify that the discussions had run into major problems. They predicted that enough progress would be registered by the weekend to justify extending the talks into a second week.
The Cook-Vedrine mission is likely to be followed by a visit by Madeleine Albright, United States Secretary of State, and by a ministerial meeting of the Contact Group of leading powers, to review progress.
No one is pretending that the negotiations will be anything other than fiendishly difficult. With the two sides refusing direct, face-to-face discussions, the international mediators, led by Christopher Hill, the US ambassador to Macedonia, are conducting "proximity talks", relaying positions, demands and concessions between the two delegations.
Having studied draft peace proposals drawn up by mediators, the Serbs and Albanians are now being pressed to consider key issues, including the juridical status of the province for the three years an "interim agreement' would run, and the procedures for proposed elections of a Kosovo assembly.
Earlier, a Serb official was quoted as describing the proposals for greater Kosovo autonomy as "horrifying".
Beyond that loom problems over the proposed 30,000-strong Nato peacekeeping force for Kosovo. The Serbs are opposed to such an intrusion onto its sovereign territory. But the Albanians want no less than Nato's signature on a peace deal.Reuse content