Azerbaijan's Defence Ministry said on Saturday that one of its servicemen was killed by sniper fire from Armenian forces in the border district of Kalbajar, but the alleged incident was swiftly refuted by Armenia.
Interfax news agency cited the Armenian Defence Ministry as saying the report was incorrect, without giving further details.
The conflicting statements came as a mass exodus of ethnic Armenians continued from the region of Nagorno-Karabakh after Azerbaijan defeated this month the breakaway region's fighters in a conflict dating from the Soviet era.
More than 100,000 of some 120,000 of ethnic Armenians have already left the region for Armenia, according to the head of the U.N. refugee agency (UNHCR).
Azerbaijan, which has repeatedly denied any claims of ethnic cleansing, said that the rights of Armenians in Karabakh, a territory internationally recognized as part of Azerbaijan, would be guaranteed.