Apologies from Iranian leaders over the downing of an airliner on January 8 have done little to quell mass anti-government protests spreading across the country.

Thousands of demonstrators hit the streets on January 11-12 condemning Iranian authorities for shooting down a Ukrainian passenger plane and killing all 176 people on board, CNN reports.

The airliner disaster came hours after Iran fired missiles at Iraqi military bases housing US troops. That was retaliation for a drone strike at Baghdad airport that killed Iranian commander Qasem Soleimani.

Amid rising tensions in the region, eight Katyusha rockets hit Iraq's Balad Air Base, north of Baghdad, on Sunday, wounding four Iraqi air force officers, the Iraqi military said in a statement. No American or coalition forces were at the base when the rockets struck, a US military official said.

In Iran, demonstrators are calling for Supreme Leader Ayatollah Ali Khamenei to step down and for those responsible for downing the plane to be prosecuted.

"Khamenei have shame. Leave the country," chanted protesters in the capital, Tehran, in footage posted on social media.

Khamenei has been in office for three decades, and there is no limit to his term.

Protests have now spread to other cities, including Shiraz, Esfahan, Hamedan and Orumiyeh, Reuters reported.