"Azerbaijan, showing good will, has decided to unilaterally cease hostilities", Azerbaijan's defense ministry said in a statement, warning it would "liberate all (Armenian-) occupied territories" if Armenian forces "do not stop provocations."
Baku also pledged to "reinforce" several strategic positions it said it had "liberated" inside the region, which is controlled by Armenia but internationally recognised as part of Azerbaijan.
But spokesman for the Armenian-backed rebel defense ministry in Karabakh, David Babayan, told AFP that fighting has never been halted along the frontline.
Earlier on Sunday, Karabakh forces claimed they took back the strategic Lala-Tepe height in Karabakh which was captured by Azeri troops on Saturday.
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Baku denied the report, saying that the height remained under its control and that rebel troops sustained "serious manpowewr losses."
On Saturday, fierce clashes left at least 18 Armenian and 12 Azerbaijani soldiers dead and reportedly claimed the lives of two civilians after both sides accused each other of attacking with heavy weaponry across the volatile frontline.
Both Russia and the West appealed to all sides to show restraint.
The foes have never signed a peace deal despite a ceasefire in 1994.
The region is still internationally recognised as part of Azerbaijan and the two sides frequently exchange fire, but the latest episode marked a surge in violence and sparked frantic appeals for peace from international powers.
Energy-rich Azerbaijan, whose military spending has in the past exceeded Armenia's entire state budget, has repeatedly threatened to take back the breakaway region by force if negotiations fail to yield results.