In capital Baghdad and southern cities, demonstrators chant "we reject Allawi" and hold posters of the new PM's face with a red cross through it a day after Mohammed Tawfiq Allawi's appointment.
The violence is the latest since protests in Iraq reignited last week after a brief lull amid soaring tensions between Washington and Tehran.
Qatari Emir Sheikh Tamim bin Hamad Al-Thani held talks with Iran's President Hassan Rouhani in Tehran.
Parliament approved the resignation without a vote, as protests continued across the country. At least one protester was killed in anti-government demonstrations in Baghdad and Iran's Najaf consulate was set ablaze for a second time on Sunday.
Iraq's parliament has approved the resignation of Prime Minister Adil Abdul Mahdi on Sunday, amid ongoing violence and anti-government demonstrations in the capital.
The most recent protests differ radically in their demands and the harsh government response has raised the stak.
Protesters stormed the Iranian consulate in Iraq's southern city of Basra on Friday, turning their wrath on Iraq's powerful neighbour after five days of deadly demonstrations in which government buildings have been ransacked and torched.
The session was held after 16 political groupings, including those of Shia cleric Muqtada al Sadr and outgoing Prime Minister Haider al Abadi, reached an accord to create the biggest bloc in parliament.
The Iraqi government is preparing for parliamentary elections in May. But much of the country is still dealing with the aftermath of the fight against Daesh.
Although the referendum cannot legally cleave Iraq into two, the results can trigger more instability in an already volatile region. The Iraqi central government and other countries have emphasised that the use of force may come into play.
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