The victims included an Armenian civilian killed in his courtyard by Azerbaijani shelling on villages along the Karabakh border, Armenian defence ministry spokesman Artsrun Hovannisian told AFP.
In a separate incident along the Karabakh frontline, a 25-year-old soldier was killed by Azerbaijani fire, the separatist enclave's defence ministry said in a statement.
The third victim was an Azerbaijani soldier killed on Thursday in a shootout with Armenian forces, the defence ministry in Baku said.
Azerbaijan and Armenia are locked in a decades-long conflict over Nagorny Karabakh, an ethnic Armenian enclave in Azerbaijan.
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Clashes between Azerbaijani and Armenian forces intensified in January following an unprecedented spiral of violence last year.
Six Armenian soldiers were reported killed last month in similar incidents on the Armenian-Azerbaijani border, and along the Karabakh frontline.
Ethnic Armenian separatists backed by Yerevan seized control of Karabakh during a 1990s war that left some 30,000 dead.
Baku, whose military spending exceeds Armenia's entire state budget, has threatened to take back the region by force if negotiations fail to yield results.