The airport said the Monday morning flights to Iran will go ahead according to schedule.
Earlier, media reports said the Azerbaijan Republic has suspended all flights from the capital Baku to Tehran without prior notice.
Azerbaijani media also said the flag carrier Azerbaijan Airlines will refund the tickets cancelled due to the development.
According to the Azeri media, the suspension of the flights would have meant all air and land access between Iran and the Azerbaijan Republic was limited to the crossing though Nakhchivan autonomous republic, as all other routes have already been blocked.
The development comes amid a war of words between Tehran and Baku over the latter’s ties with Israel, which Iran sees as a threat at its northwestern borders.
Foreign ministers of the two countries held phone talks on April 8 during which the Iranian side raised the “plot” by Israel against the solidarity, security and progress of regional countries.
During the talks the Iranian side had also called on Baku to better manage the media in line with the interests of the two countries.
Tensions between Iran and Azerbaijan have been steadily ramping up in recent months.
In late January, a man stormed the Azerbaijani embassy Tehran, killing its head of security and wounding others.
Investigations in Iran found the attacker had personal motives, but Baku blamed the Iranian government and later expelled a number of Iranian diplomats in April.
In a tit-for-tat move, Iran expelled four Azerbaijani diplomats last month.