The clashes on Tuesday along the Caucasus neighbours' shared border were the worst since they went to war last year over Karabakh and sparked fears of another flare-up in their long-running territorial dispute.
"Six Armenian troops were killed in action as a result of an attack by Azerbaijani armed forces," the Armenian defence ministry said in a brief statement.
It had earlier this week reported one death and said 13 Armenian soldiers were captured by Azerbaijani forces while 24 more servicemen were missing.
Azerbaijan said earlier this week that seven of its troops were killed and 10 more wounded after Armenia provoked clashes.
A ceasefire was reached Tuesday evening following mediation by Russia's Defence Minister Sergei Shoigu and has held since.
Last year's six-week conflict, which claimed the lives of more than 6,500 people, ended in November in a Russia-mediated deal that saw Armenia cede swathes of territory it had controlled for decades.
Ethnic Armenian separatists in Nagorno-Karabakh broke away from Azerbaijan as the Soviet Union collapsed in 1991, and an ensuing conflict claimed around 30,000 lives.