The Armenian Ministry of Defense said in a statement on Tuesday that four military personnel were killed and one was wounded during the shelling from the Azerbaijani side on the border.
Azerbaijani armed forces discharged fire toward the Armenian combat positions in the vicinity of Nerkin Hand, southern Armenia's Syunik region, between 5:30 a.m. and 9:30 a.m. local time, according to the Armenian Ministry of Defense.
Azerbaijan's border guards said the move was in response to Armenian troops opening fire twice late on Monday on Kokhanabi village in the northeastern Tovuz region.
Armenia denied the allegation, saying the claim that its troops had twice "fired against the direction of Azerbaijani positions situated in the northeastern part of the border does not align with reality."
Russia on Tuesday called on Armenia and Azerbaijan to show restraint after the shelling in the morning caused deaths and casualties, which is the most serious fighting in the region since last September.
Russia, which is formally allied to Armenia but also has close ties to Azerbaijan, has a contingent of peacekeepers deployed in the region, and its border guards patrol Armenia's frontiers.