The two sides were accused of violating a new humanitarian ceasefire on Sunday, when they fought over the Nagorno-Karabakh mountain enclave, hours after it had been agreed.
Saturday, after a week-old Russian-brokers' ceasefire, the truce entered into force at midnight (2000 GMT) without stopping the worst fighting in the South Caucasus since the 90s.
The Armenian Ministry of Defence said the Azerbaijani army fired and used artillery twice in the night.
The Azerbaijani forces had started an attack on the military position of the enclave and were wounded on both sides by victims and by officials in Nagorno-Karabakh.
"An enemy fired near to the city of Jabrail, and villages of this region," said the Azerbaijani Defense Ministry. Use of artillery and mortar. The Azerbaijani army has "taken appropriate repressive measures."
This month's ceasefire sought to allow the sides to swap prisoners and bodies of the people killed during the clashes, but it had little impact on the struggle around the enclave.
The new truce was announced on Saturday after Russian Foreign Minister Sergei Lavrov had spoken with his Armenian and Azerbaijani counterparts by phone.
Russia, France, and the United States belong to the Minsk Group, which tried to assist in solving the conflict under the auspices of the OSCE.
Baku said Saturday that since the war flared on 27 September 60 Azerbaijani civilians have been killed and 270 wounded. It did not reveal its military victims.
Nagorno-Karabakh reports that 633 military staff and 36 civilians have been murdered.