Two soldiers from Azerbaijan and Armenia have been killed in shootings just after the two countries' presidents renewed commitment to a truce in the disputed Karabakh region.
Armenian and Azerbaijani Presidents Serzh Sarksyan and Ilham Aliyev met in Vienna on Monday following a resurgence in violence which has killed dozens of people in recent weeks.
In a joint statement, the US, Russia and France said the two presidents "reiterated their commitment to the ceasefire and the peaceful settlement of the conflict."
However, Armenian-backed forces in Karabakh said a fighter was killed just after midnight on Tuesday as a result of shooting from Azerbaijan's side.
Azerbaijan's Defense Ministry said an Azeri soldier was also killed "in a ceasefire violation."
Azerbaijan and separatists backed by Armenia fought a war over Karabakh in the early 1990s, with thousands killed on both sides and hundreds of thousands displaced.
There has been sporadic violence since the war ended with a truce in 1994.
Last month, the two countries came to the brink of another war following exchange of heavy fire with artillery, tanks, rockets and helicopters which killed at least 110 people.
Russian Foreign Minister Sergei Lavrov said following the Monday meeting that he sensed there was now a desire on both sides for a compromise.
The joint statement said Sarksyan and Aliyev agreed to fix a time and place for their next meeting in June.
The Organization for Security and Cooperation in Europe (OSCE), it said, would quickly finalize a plan to monitor the ceasefire in Karabakh.
Ethnic Armenians in Karabakh broke away from Azerbaijan in 1988 and declared themselves a republic, sparking a war which claimed over 30,000 lives.
As a result of the conflict, ethnic Azerbaijanis fled the territory which constitutes about 20% of the country.
The region, which is located in Azerbaijan, has been under the control of local ethnic Armenians since then but it is regarded part of Azerbaijan by the United Nations.
The recent surge in conflict has worried Europe because it could cause instability in a region that serves as a corridor for pipelines taking oil and gas to world markets.