Both sides agreed had agreed a truce to start at midnight local time (20:00 GMT Saturday).
But an Armenian defence ministry spokeswoman said Azerbaijan broke the ceasefire after just four minutes by firing artillery shells and rockets.
Azerbaijan later said Armenia had broken the truce after two minutes.
Both countries signed a Russian-brokered ceasefire last Saturday. However, clashes continued despite that accord.
Fighting flared last month over the territory, which is internationally recognised as part of Azerbaijan but run by ethnic Armenians. Hundreds have died.