The two former Soviet republics have long been in conflict over Azerbaijan's breakaway, mainly ethnic Armenian region of Nagorno-Karabakh, although the latest clashes occurred some 300 km (190 miles) from the mountainous enclave.
The Azeri defence ministry said four of its soldiers were killed and five wounded while Armenia's ministry said that two of its soldiers were wounded. The two sides traded accusations of ceasefire violations and firing artillery.
Exchanges of fire began on Sunday and continued into Monday in the rugged South Caucasus region.
Though a ceasefire was agreed in 1994, Azerbaijan and Armenia continue to accuse each other of shooting attacks around Nagorno-Karabakh and along the separate Azeri-Armenian frontier.
The frozen Nagorno-Karabakh conflict has concerned the international community in part because of its threat to stability in a region that serves as a corridor for pipelines taking oil and gas to world markets.