The meeting of the presidents of Azerbaijan and Armenia, Ilham Aliyev and Serzh Sargsyan ended in Vienna.
The presidents left the Palais Coburg hotel, without giving any comments to the press.
A source in the delegation of one of the states told RIA Novosti that the OSCE Minsk Group is expected to issue a statement as a result of the meeting.
This is the first meeting between the two presidents in two years.
The conflict between the two South Caucasus countries began in 1988 when Armenia made territorial claims against Azerbaijan.
Armenian armed forces have occupied 20 per cent of Azerbaijan since 1992, including the Nagorno-Karabakh region and seven surrounding districts.
Azerbaijan and Armenia signed a ceasefire agreement in 1994. The co-chairs of the THE OSCE Minsk Group, Russia, France and the U.S. are currently holding peace negotiations.
Armenia has not yet implemented the U.N. Security Council's four resolutions on the liberation of the Nagorno-Karabakh and the surrounding regions.