The alleged incident is the latest tragedy to take place in the most volatile section of Armenia's heavily militarized border with Azerbaijan.
Yerevan had said its soldiers died while fighting off a cross-border incursion by Azerbaijani forces into Armenia's Tavush region.
"The sabotage advance was halted and the enemy was repelled, suffering casualties," read an Armenian Defense Ministry statement. "The Armenian Armed Forces control the situation along the line of contact, carrying out actions commensurate with the situation," it said without providing details.
The statement added that Armenia's chief military prosecutor, Gevorg Kostanian, and a team of Defense Ministry investigators rushed to the scene.
The Azerbaijani military was quick to deny shooting Armenian troops at what is the westernmost section of the roughly 1,000-kilometer Armenian-Azerbaijani frontier. The Trend news agency quoted a spokesman for the Defense Ministry in Baku alleging that the soldiers had been gunned down by their Armenian comrades.
The situation along that border section has been tense in recent months, with both warring sides reporting cease-fire violations on a regular basis. Three other Armenian soldiers were killed in the area just over a month ago. The Armenian military pledged to take retaliatory actions at the time amid renewed international concerns over the possible outbreak of a full-scale war in the conflict over the breakaway Azerbaijani region of Nagorno-Karabakh.
The latest deaths come just three days after field representatives of the Organization for Security and Cooperation in Europe (OSCE) monitored the cease-fire regime in Tavush and an adjacent region in western Azerbaijan. A civilian resident in the Armenian village of Aygepar was reportedly wounded there late last week.
Later on June 4, U.S. Secretary of State Hillary Clinton arrived in Yerevan for talks with Armenian leaders. She was expected to discuss the Nagorno-Karabkh conflict.
Clinton is due to visit Azerbaijan on June 6.