Tehran hit the headquarters of the Kurdistan Democratic Party of Iran (KDPI) outside the cities of Erbil and Sulaimaniyah in Iraq’s self-ruled Kurdistan region with missiles, artillery fire and drones.
At least one person was killed and 10 others wounded, local officials said.
Iran's Revolutionary Guard Corps (IRGC) said it had fired at the bases of “terrorist groups” in the Kurdish region.
“We strongly condemn Iran’s continued missile and drone attacks against the Iraqi Kurdistan Region,” US Department of State spokesman Ned Price said on Monday.
Mr Price said Iran “has repeatedly and brazenly violated Iraq’s sovereignty”, calling for an end to the attacks and refrain from “further threats against Iraq’s territorial integrity”.
He said the US “stands with our partners in Baghdad and Erbil and shares the government of Iraq’s objective to preserve the country’s security, stability and sovereignty”.
The Arab Parliament, the legislative body of the Arab League, described the attack as “brute and a flagrant violation to all international conventions and norms, the sovereignty of Iraq and the principles of good neighbouring”.
It expressed support to Iraq to “achieve stability, security and to preserve its sovereignty”.
Iran released video of the strikes through its semi-official news agency Tasnim on Monday.
The attacks were latest in a series of strikes Iran has been launching against the armed Kurdish opposition groups based in northern Iraq since September.
It has accused them of fanning the continuing protests across the country.
The Iranian regime has been struggling to contain widespread anti-government demonstrations ignited by a young woman's death in police custody.
The death of Mahsa Amini, 22, who was detained by the country's morality police in Tehran, triggered unrest in the capital and Iran's provinces.
Amini’s family is from Iran’s western Kurdish region, which borders Iraq.