The Armenian Ministry of Defense also said four military personnel had been injured.
The Azerbaijani army has reported that two of its soldiers have been wounded, but has not confirmed the deaths.
The clashes broke out the previous day in two places along the border.
Azerbaijan reported that Armenian forces had fired on workers building the fortifications.
Today, the two countries have insulted each other in the use of small arms and artillery.
In September last year, war broke out between Armenia and Azerbaijan over the Armenian-populated disputed region of Nagorno-Karabakh, killing some 6,500 people.
The war lasted six weeks and ended on November 9, when Armenia and Azerbaijan, with Russian support, signed an agreement to cease fire in the Nagorno-Karabakh conflict, which many see in Armenia as a capitulation.
Under the agreement, Armenians lost part of Nagorno-Karabakh’s main territory, as well as all areas of the security buffer zone that had been under Armenian control since the 1990s.
Nagorno-Karabakh, which was part of the Azerbaijani SSR during the Soviet era, has been a “de facto” independent Republic of Armenia since the early 1990s. Although Azerbaijan has not controlled Nagorno-Karabakh since the collapse of the USSR, it considers the Armenian region to be its territory.
