Azerbaijan's Defence Ministry said that 12 of its troops have been killed in the past four days, including four overnight.
Nagorno-Karabakh's armed forces said one of its soldiers was killed, the third in recent days.
Azerbaijan's Nagorno-Karabakh region and some adjacent territory have been under the control of Armenian soldiers and ethnic Armenian local troops since the end of a six-year separatist war in 1994.
Both sides report frequent attacks along the cease-fire line, but the latest outbreak of fighting is the worst in many years.