At least one person was killed when several Iranian missiles struck the headquarters of the Kurdistan Democratic Party of Iran (KDPI) in northern Iraq on Monday morning.
Ten others were wounded, said the mayor of the city of Koya, Tariq Haydari.
Koya is near Erbil, the regional capital of Iraq's self-ruled Kurdistan region.
Mr Haydari put the number of missiles at five. The casualty figures are likely to increase, he said.
Tehran confirmed the strike in a brief statement carried by the semi-official Fars news agency.
Iran released video of the strikes through its semi-official news agency Tasnim.
It said Iran's Islamic Revolutionary Guard Corps had fired at the bases of “terrorist groups” in the Kurdish region of Iraq with missiles and drones.
The UN mission to Iraq condemned the attacks, saying they “violate Iraqi sovereignty”.
“Iraq should not be used as an arena to settle scores and its territorial integrity must be respected,” the UN said.
“Dialogue between Iraq and Iran over mutual security concerns is the only way forward.”
Later on Monday, Iraq's Foreign Ministry “condemned with strongest terms” the strikes, saying it would respond with “high-level diplomatic measures”.
It said the attacks were a “blatant violation of Iraq’s sovereignty and the security of its citizens”.
The ministry said Iraqi Foreign Minister Fuad Hussein discussed the attacks with Iran's Hossein Amirabdollahian by phone.
During the call, Mr Hussein stressed the “importance of dialogue as a way to stop this unjustified hostile escalation, describing the continuation of these unilateral actions as dangerous”.
The Kurdish group is a leftist armed opposition force banned in Iran.
The KDPI declared war against the Iranian government after the 1979 revolution and is among several Iranian Kurdish parties whose fighters attack Iranian and Turkish forces from their bases in the mountainous border areas of Iraqi Kurdistan.
Iran has been attacking the armed Kurdish opposition groups based in northern Iraq since September, accusing them of fanning the continuing protests across the country. It has used artillery fire, missiles and drones.
Since then, 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 bordering Iraq.
