Armenia says three of its soldiers have been killed in an exchange of gunfire with Azerbaijan and the Interfax news agency reports that Baku had later accepted a Russian ceasefire proposal to try to calm tensions.
Armenia's defence ministry said in a statement that Azeri forces had attacked Armenian positions near the border between the two countries.
Two Armenian servicemen had been injured in the same incident, it said, and "fighting continued".
Azerbaijan's defence ministry accused Armenian forces of what it called "provocations" in the Kalbajar district and said its army would continue to retaliate, Russia's TASS news agency reported.
Interfax later reported that Azerbaijan had however accepted a Russian proposal to enforce a ceasefire in the area.
The incident was one of the deadliest since a six-week war between ethnic Armenian forces and Baku over the Nagorno-Karabakh region and surrounding areas ended last year.
In six weeks of fighting last September to November, Azeri troops drove ethnic Armenian forces out of swathes of territory they had controlled since the 1990s in and around the Nagorno-Karabakh region, before Russia brokered a ceasefire.
A simmering border dispute between the two has since flared up, with both sides accusing each other of separate incursions into each others' territory in recent months, highlighting the fragility of the ceasefire.
Australian Associated Press