Washington: The United States is closely monitoring Iraqi forces in Tikrit amid allegations of human rights abuses committed by Baghdad's troops and allied fighters in an assault to retake the city, a US military official said Thursday.

It was "unclear" if executions and other alleged atrocities had taken place, the senior military official told reporters, but "that's exactly what we're going to be watching" for as Iraqi forces move to secure Tikrit.

Iraqi troops backed by paramilitary groups and US-led air strikes took back Tikrit from the Daesh group last week.

Rights violations reported

Amnesty International said Thursday it was investigating reports of serious rights violations during the Tikrit offensive, including allegations of executions, abductions and the burning and looting of homes.

The United States agreed to provide air power to back up the assault on the Daesh in Tikrit after the Iraqi government assured Washington it had full control over all forces involved in the operation. That required some militias with ties to Iran to pull back from attacks on the Tikrit town centre.

The decision to provide US-led air raids demonstrated Washington's support for the Iraqi government, the military official said.

But the Iraqis "need to understand we will hold them accountable for the aftermath of the Tikrit operation," said the official, who spoke on condition of anonymity.

The government in Baghdad will need to fulfill its promises to turn the city over to police, to respect the rights of Sunnis in the area and to deliver prompt humanitarian and reconstruction assistance, the official said.

"We're watching them very carefully, once the city is completely under control of the central government, whether the central government lives up to its commitment," the official said.

The United States and rights groups have repeatedly warned that any abuses will only sow the seeds of future violence and play into the hands of the Daesh.

Next battle: Baiji

In Tikrit, Iraqi forces still face "pockets" of resistance from the Daesh group and "they are working there through those pockets," the official said.

Once the Tikrit military operation is complete, "the next step is Baiji," the official said.

The town of Baiji lies north of Tikrit along the Tigris River and remains under the Daesh group's control.

"That's really the next significant military manoeuvre because, of course, the Baiji oil refinery is important to the Iraqi economy," the official said.

The nearby Baiji refinery was recaptured by Iraqi forces last year but Baghdad still needs to dislodge the Daesh extremists from the town and surrounding areas, the official said.

An offensive in Baiji is a necessary step towards an eventual large-scale operation to seize back Mosul, the country's second-largest city and a bastion for the Daesh group.

But an offensive to recapture Mosul is several months away and likely will not come before the autumn, the official said.

No operation in Mosul was expected to be carried out during Ramadan, which falls in mid-June, or during the summer months when intense heat would hamper any major military action, the official said.

A potential offensive is likely "to extend into the fall for reasons of Ramadan preparation and weather," he said.

A US defense official had predicted in February that an Iraqi assault in Mosul could come as soon as April or May but top Pentagon officials later backed away from that forecast.

Last November, Iraqi security forces backed by Shi'ite paramilitary groups managed to break a months-long siege of the Baiji refinery that had forced it to shut down operations.

Victory in Tikrit

The Iraqi government claimed victory over Daesh insurgents in Tikrit on Wednesday after a month-long battle for the city supported by militiamen and US-led air strikes, saying that only small pockets of resistance remained.

The militants captured the city, about 140 km (90 miles) north of Baghdad, last June as they swept through most of Iraq's Sunni Muslim territories.