Azerbaijani army cleared several "advantageous high grounds" around the Talysh village of the occupying Armenian forces, the country's Defense Ministry said in a statement on Monday.
Border clashes broke out early Sunday when the Armenian forces targeted Azerbaijani civilian settlements and military positions, leading to casualties.
"Units of the Azerbaijan Army, moving from the high grounds and advantageous positions liberated from the Armenian armed forces, continue the counter-attack to consolidate the achieved success," the ministry said.
The written statement also said that a large number of Armenian forces have been killed, adding "the enemy" suffered heavy losses.
"By inflicting rocket-artillery and airstrikes on enemy positions, he was forced to retreat from the frontiers he was trying to hold," it added.
Relations between the two former Soviet nations have been tense since 1991, when the Armenian military occupied Upper Karabakh, or Nagorno-Karabakh, an internationally recognized territory of Azerbaijan.
Four UN Security Council and two UN General Assembly resolutions as well as many international organizations demand the withdrawal of the occupying forces.
The OSCE Minsk Group-co-chaired by France, Russia and the US-was formed in 1992 to find a peaceful solution to the conflict, but to no avail. A cease-fire, however, was declared in 1994.