Armenian Prime Minister Nikol Pashinyan accused Azerbaijan's troops on Monday of violating the border between the two countries and sacked his defense minister, the Interfax news agency reported.
Another Russian news agency, RIA, quoted Armenia's Security Council as saying the incident took place on Sunday but the Azeri troops had since left.
Interfax quoted an Azeri foreign ministry spokesperson as saying Azeri forces were operating on the country's own sovereign territory and accusing Armenia of "provocations."
The incident marked an escalation of tensions between the two former Soviet republics, which fought a 44-day war last year that killed at least 6,500 people and ended in a decisive victory for Azerbaijan.
Pashinyan did not say on what scale the alleged incursion had taken place but told a security council meeting that he had dismissed minister Arshak Karapetyan over the incident.
TASS news agency said Armenia had reported the episode to Russia and the Collective Security Treaty Organization, a military alliance of post-Soviet states.
Last year's war over the enclave of Nagorno-Karabakh was ended by a Russian-brokered deal under which Moscow deployed 1,960 peacekeepers to the region for an initial five-year period.
But the accord left many questions unresolved, including the legal status of Nagorno-Karabakh and the Armenians who live there, who numbered up to 150,000 before the war.