The ministry said in a statement the troops were killed in a fight after Armenian troops tried to enter a village in northwestern Azerbaijan, RIA Novosti reported.
The Armenia-Azerbaijan conflict began in the late 1980s when Nagorno-Karabakh -- a region with a predominantly ethnic Armenian population -- declared its independence from Azerbaijan. The region has been under Armenian control since.
Armenian and Azerbaijani foreign ministers have agreed to hold talks on Nagorno-Karabakh June 18 in Paris, RIA Novosti said. Russia has been mediating peace talks for years.
U.S. Secretary of State Hillary Clinton during a visit at Yerevan, Armenia, condemned the border clashes Monday, saying the use of force "will not resolve the Nagorno-Karabakh conflict."
"I am very concerned about the danger of escalation of tensions and the senseless deaths of young soldiers and innocent civilians," she said during her visit to the North Caucasus states.
Clinton said such incidents "underscore the necessity to try to keep making progress on the peace process. … And it's not only the actions of leaders; it must be the actions of citizens as well to try to find a way to enable people of the region to live together in peace and dignity."