Haider al-Abadi said those who caused damage and attacked police should be brought to justice.
The demonstrators, supporters of Shia cleric Moqtada Sadr, were angered by delays in approving a new cabinet.
They are now camped out near parliament, demanding a change in government.
Protesters have accused the government of neglecting much-needed reforms, as it struggles with its campaign against the so-called Islamic State group and declining oil revenues.
IS, a Sunni Muslim group that controls parts of western and northern Iraq, claimed a twin suicide bombing on Sunday that killed at least 33 people and wounded more than 50 in the southern town of Samawa.
Supporters of Mr Sadr want MPs to push through plans to replace ministers with political affiliations with non-partisan technocrats.
Powerful parties in parliament have refused to approve the change for several weeks.
‘We need new faces’
Mr Abadi issued his arrest order after touring the Green Zone on Saturday. The zone, a highly fortified area 10 sq km (3.9 sq miles) in size, is home to key government buildings and foreign embassies.
It is ringed by blast walls, some of which were toppled by the protesters as they breached the zone for the first time in weeks of civil unrest.
There are no indications that any actual arrests have taken place.
Saturday’s occupation of parliament came after MPs again failed to reach a quorum to vote on the cabinet changes.
After the protest, demonstrators set up camp outside the parliament, and many were still there on Sunday.
“We need new faces not the old ones,” female protester Shatha Jumaa, a 58-year-old surgeon who described herself as a secularist, told the Associated Press news agency.
She said she wanted the current government dissolved and replaced by a small interim administration whose job would be to amend the constitution and to prepare for an early national election.
Mr Abadi, who came to power in 2014, has promised to stamp out corruption and ease sectarian tensions.
Iraq’s system of sharing government jobs has long been criticised for promoting unqualified candidates and encouraging corruption.
The government is carefully balanced between party and religious loyalties but the country ranks 161st of 168 on corruption watchdog Transparency International’s corruption perceptions index.
Few details were immediately available about the double bombing in Samawa. Police say the blasts came within minutes of each other, the first outside a local government office, the second at a bus station.
IS said it had targeted police in the mainly Shia town, about 240km (148 miles) south-east of the capital.
The country has been riven for years by deadly sectarian violence between the Shia majority and Sunnis