Armenian President Serzh Sarkisian said 18 Armenian troops were killed and some 35 wounded in the "largest-scale hostilities" since a 1994 truce ended a war that saw Armenian-backed fighters seize the territory from Azerbaijan.
Sarkisian did not specify if the troops were from the forces of unrecognised Karabakh -- which claims independence but is backed by Yerevan -- or Armenia's army.
Earlier Azerbaijan's defence ministry said that 12 of its soldiers were killed in the clashes and a military helicopter shot down.
Armenia accused Azerbaijan of launching a "massive attack along the Karabakh frontline using tanks, artillery, and helicopters" on Friday night.
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Azerbaijan, however, insisted it had counter-attacked after coming under fire from "large-calibre artillery and grenade-launchers".
Sarkisian said that clashes were continuing Saturday evening "in the north and south" of the frontline but insisted the "armed forces of Karabakh are in control of the situation."
Ethnic Armenian separatists backed by Yerevan seized control of the mountainous Nagorny Karabakh region in the early 1990s war that claimed some 30,000 lives and the foes have never signed a peace deal despite the 1994 ceasfire.
Azeri forces claimed that they had taken control of several strategic heights and a village in the Armenian-controlled territory, but Yerevan denied the claim as "disinformation".
Russian President Vladimir Putin called for an immediate end to fighting along the frontline, the Kremlin said.
"President Putin calls on the parties in the conflict to observe an immediate ceasefire and exercise restraint in order to prevent further casualties," Kremlin spokesman Dmitry Peskov told Russian news agencies.