Armenian police say three civilians have been killed by artillery and gunfire from Azerbaijani forces.
The deaths, along with the wounding of two civilians, occurred in several villages in Armenia's Tavush region near the countries' border.
There was no immediate comment by Azerbaijan to the claim on September 25.
But that country's Defense Ministry said earlier that Azerbaijani villages in the area had come under fire and that its armed forces responded.
The two former Soviet republics remain hostile more than 20 years after a cease-fire was called in the conflict over Nagorno-Karabakh, a predominantly Armenian region of Azerbaijan.
The region is now under the control of local ethnic Armenian forces and the Armenian military.
Each side frequently accuses the other of violating the truce. Sporadic clashes between the two have thwarted international efforts to find a permanent solution to the dispute that broke out in the dying years of the Soviet Union and has killed about 30,000 people.