Several missiles were fired at dawn on Sunday at Arbil, the capital of autonomous Kurdistan in northern Iraq, local authorities reported, adding there were no injuries.
“Several missiles fell on the city of Arbil,” said governor Omid Khoshnaw, quoted by the Iraqi news agency INA.
The governor said it was not clear whether the intended target was the US consulate or the airport, where there is a base for the US-led coalition fighting the Islamic State group.
An AFP correspondent in Arbil heard three explosions.
Local television channel Kurdistan24, whose studios are not far from the US consulate, posted images on social networks of its damaged offices, with collapsed sections of false ceiling and broken glass.
The health ministry in Arbil said there had been no casualties.
The airport said it had suffered no damage and flights had not been disrupted.
“We condemn this terrorist attack launched against several sectors of Arbil, we call on the inhabitants to remain calm,” Kurdistan Prime Minister Masrour Barzani said in a statement.
US interests and coalition troops in Iraq have regularly been targeted in rocket and armed drone attacks.
Western officials have blamed hard-line pro-Iran factions for the attacks, which have never been claimed.
In late January, six rockets were fired at Baghdad International Airport, causing no casualties.
Iraq saw a surge in these sort of attacks at the beginning of the year as Iran and its allies commemorated the second anniversary of the death of Iranian general Qassem Soleimani and his Iraqi lieutenant Abu Mehdi al-Mouhandis, killed by American drone fire in Iraq in January 2020.