Azerbaijan and Turkey have sought to establish a transport corridor linking the two countries via an enclave in the area, which both Iran and Armenia strongly oppose.
Morteza Abedin Varamin, Iran's new consul-general in Kapan, appeared to fire off a warning to Azerbaijan and Turkey during the inaugural opening.
"I will advise the people of Kapan not to worry, we are here for the Armenian people," Morteza Abedin Varamin said, according to Al Jazeera.
Iran has strongly opposed the proposed Zangezur Corridor which would link the Azeri enclave of Nakhchivan with Azerbaijan proper.
The corridor, which would bypass Armenian checkpoints, would effectively cut a major Iranian southern Caucasus transport link, Al Jazeera reported.
Shia-majority Iran and Azerbaijan have testy relations, in part due to Baku's close ties with Israel.
Iran and Armenia have become increasingly close in recent years, coinciding with war between Yerevan and Baku over the Nagorno-Karabakh region.
Iran has recently conducted military drills on its border with Azerbaijan and the consulate move appears to be a ratcheting of tensions between the two countries.
"Iran considers Armenia's security to be the security of its own and the region," said FM Amirabdollahian.
Tehran has also invited Armenia to open a consulate in Tabriz, a city in an Azerbaijani-speaking area.