"We believe that such negotiations serve as a warranty for peace, stability and opening new opportunities for regional co-operation," Ukrainian Foreign Minister Leonid Kozhara, a regional chairman for the Organization for Security and Cooperation in Europe, said in a statement Tuesday.
Armenia and Azerbaijan have fought repeatedly over the disputed territory. Both sides exchanged fire over Nagorno-Karabakh last year.
"I trust that the highest-level dialogue between Armenia and Azerbaijan will contribute to strengthening confidence and mutual understanding between the parties and will provide a positive incentive for the negotiation process on the Nagorno-Karabakh conflict settlement," the Ukrainian minister said.
The Minsk Group of the OSCE chaired the meeting in Vienna. It issued no statement about the outcome of the talks but said the two presidents met in private to discuss a "broad range of issues" related to the Nagorno-Karabakh conflict.
Both sides, the OSCE said in a statement, agreed to future talks about a peaceful settlement.