Iraq's prime minister said Monday that "only" 152 homes and shops were burned in Tikrit, where pro-government forces have been accused of carrying out abuses after retaking the city.

Haider al-Abadi did not specify who burned the structures or when the fires took place, but pro-government militiamen have admitted to torching houses in other recaptured areas and allegedly did so in Tikrit as well.

Security forces and allied paramilitaries retook the city last week from the Islamic State (IS) group, which overran large parts of the country last year, but misconduct has marred Baghdad's biggest victory yet over the jihadists.

"Only 67 houses and... around 85 stores were burned, and it is a very small number for a city with a population of 100,000 people," Abadi told a news conference in the Iraqi Kurdish regional capital Arbil.

He said those figures were confirmed by top officials including the governor and police chief of Salaheddin province, of which Tikrit is the capital.

Columns of black smoke rose from burning homes and shops even as Abadi visited Tikrit last Wednesday to celebrate its recapture from IS.

During the visit, pro-government militiamen looted and put graffiti on shops in central Tikrit while journalists looked on.

The premier's office said Friday he had ordered security forces to "deal with cases of vandalism" in Tikrit, blaming it on "gangs" seeking to tarnish the achievements of government forces and their paramilitary allies.

Grand Ayatollah Ali al-Sistani, Iraq's top Shiite cleric who is revered by millions, urged the forces to "preserve and guard citizens' properties in areas that have been liberated".

Doing so is a "religious and national and moral duty," Sistani said in remarks read at Friday prayers in Karbala.

Additionally, "it has an important role in encouraging those who have not yet decided to participate in liberating their areas to decide to participate," he said.

"This is an important gain for all."