At least two Sunni Muslim mosques have been attacked in Iraq and two people killed in apparent retaliation for the execution of a senior Shiite cleric in Sunni-ruled Saudi Arabia, officials and police said on Monday.

Iraqi Shiites protesting the Jan. 2 execution of Saudi Shiite cleric Nimr al-Nimr separately marched in Baghdad and southern cities, while a powerful Iranian-backed Shiite militia group pressured the government to sever ties with Riyadh.

Iraq's Interior Ministry confirmed the attacks on Sunni mosques late Sunday in Hilla, around 100 km (60 miles) south of Baghdad. Prime Minister Haider al-Abadi blamed them on "Daesh (Islamic State) and those who are similar to them," without further explanation.