This was the first time the presidents and prime ministers of Serbia and Kosovo attended the negotiations.
Asked by the press about headway in the negotiations, UN special envoy for Kosovo Martti Ahtisaari said this was the first such meeting and that it would be completely wrong to expect progress.
Today's negotiations showed the two sides' diametrically opposed positions, he said, adding the meeting provided the two sides with an opportunity to explain their views.
Ahtisaari said his impression was that progress was possible, but that the two sides had to agree. He added the talks were held in a good atmosphere and that the next meeting, on a technical level, would be held in early August.
Serbian President Boris Tadic said the talks were good and that different views of Kosovo's future were expressed. "I didn't even expect the differences to be smaller, but what I heard is the basis for negotiating until a compromise (is reached)."
Serbian Prime Minister Vojislav Kostunica said Serbia proposed "essential autonomy for Kosovo, which is an open solution and can be changed, which does not go for the independence demanded by Kosovo Albanians. Serbia does not want to rule Kosovo, but is against independence".
Kosovo President Fatmir Sejdiu said Kosovo wanted "full independence, which is the desire of the majority of Kosovo's population. Thus we shall contribute to the security of Kosovo and the entire region".
He said Serbia's proposals were unacceptable for the Kosovo side. "They want to set the rules and our position is that we ourselves set the rules based on rights, laws, European values and international law."
Kosovo Prime Minister Agim Qeku said the negotiations were necessary so that "a solution could be found as soon as possible... and that is independence".
"The arguments are on our side. Primarily, the victims and suffering of our people through the centuries. The autonomy we had in the former Yugoslavia was forcibly taken away. We liberated Kosovo and the international community knows this," said Qeku, adding it was their "obligation to guarantee all the rights and security for the Serb minority in Kosovo".
The Contact Group called on both sides in a statement to be more flexible and ready to reach a comprise.