Iran has been rocked by almost two months of protests sparked by the death of Kurdish Iranian woman Mahsa Amini, 22, after she was arrested by the feared morality police for allegedly breaching the strict dress code for women.

Tehran, accusing Kurdish-Iranian opposition groups based in northern Iraq of stoking the "riots", previously launched attacks in late September that killed more than a dozen people in Iraq's autonomous Kurdistan region.

In Monday's barrage, "five Iranian missiles targeted a building used by the Kurdistan Democratic Party of Iran", the mayor of Koysanjaq in Iraqi Kurdistan, Tariq al-Haidari, told AFP.

The region's health ministry said "one person is dead and eight were wounded".

Plumes of black smoke could be seen billowing into the sky after the strikes, in videos shared on social media, as more missiles rained down on targets elsewhere in the mountainous Kurdistan region.

In Iran, a commander of the Islamic Revolutionary Guard Corps, General Osanlou, confirmed that "we struck targets located along the border and 80 kilometres (50 miles) from the border" with missiles and drones.

He charged that those targeted "were terrorists that have been active in the riots these last few months", speaking on state television about the nationwide protests.

Osanlou warned of further strikes unless Kurdistan regional authorities expel the Iranian Kurdish groups.

"We had already requested that the local government intervene but it did not do anything," he said.

A spokesman for the foreign ministry in Iran justified the cross-border military action as necessary to "preserve the security" of its territory.

- 'Rocket diplomacy' -

Another "four drone strikes" targeted bases of the Iranian Communist Party and the Iranian Kurdish nationalist group Komala in the Zrgoiz region, said Atta Seqzi, one of the leaders of Komala.

The groups had been "warned of the imminence of the strikes" and evacuated the sites, he said, adding that they had suffered "no death or injury".

One missile failed to explode but the other projectiles damaged buildings, he said.

The cross-border strikes in September saw Iraq's federal government call in the Iranian ambassador to protest the attacks and the UN mission in Iraq warn that such "rocket diplomacy is a reckless act with devastating consequences".

Iraqi Kurdistan hosts several Iranian Kurdish opposition groups which have in the past waged an armed insurrection against Tehran. In recent years their activities have declined, but the wave of protests in Iran has again stoked tensions.

The protests in Iran quickly moved beyond Kurdish areas into a broad nationwide movement that continues to rock the Islamic republic despite a state crackdown that has killed 326 people according to Oslo-based group Iran Human Rights.

Beyond the recent strikes from Iran, the Kurdish region of Iraq is also often hit by Turkish military action targeting the Kurdistan Workers' Party (PKK).

The PKK, blacklisted as a terrorist group by Ankara and its Western allies, has kept up a deadly insurgency for Kurdish self-rule in southeastern Turkey since the 1980s and maintains rear bases in Iraq.

Iraq's new Prime Minister Mohammed Shia al-Sudani, meeting journalists on Saturday in Baghdad, said that "we reject aggression from any country, whether it be Iran or Turkey" and vowed that Iraq will "take all measures" in line with international law.