"We are very concerned by reports of widespread human rights abuses committed in the course of the military operation in the area around Tikrit," the rights watchdog's Donatella Rovera told AFP.
Security forces backed by paramilitary groups and US-led air strikes recaptured Tikrit from the Islamic State group this week.
Outlying areas in Salaheddin province, which had also been under IS control since last year, were retaken gradually over the past month.
The operation was seen as a test of the Shiite-dominated forces' ability to retake a Sunni area while reining in reprisals.
"We are investigating reports that scores of residents have been seized early last month and not heard of since, and that residents' homes and businesses have been blown up or burned down after having been looted by militias," said Rovera, a senior crisis response adviser at Amnesty.
"There have also been reports of summary executions of men who may or may not have been involved in combat but who were killed after having been captured," she said.
Rovera said the latest such report was an incident Wednesday inside Tikrit.
- Burning homes -
A US military official said it was "unclear" if executions and other alleged atrocities had taken place, but stressed Iraqi forces would be closely monitored as they moved to secure Tikrit.
The Iraqis "need to understand we will hold them accountable for the aftermath of the Tikrit operation," added the official, who spoke on condition of anonymity.
Once the Tikrit military operation was complete, the next step would be to retake the town of Baiji to the north, the official said, home to an important oil refinery and currently under the IS group's control.
The Iraqi government and its coalition partners, the United Nations and rights groups have repeatedly said any military victory against IS that comes with sectarian-driven abuses would only sow the seeds of future violence.
Pro-government militiamen could be seen looting shops in central Tikrit Wednesday as Iraqi forces sought to consolidate control.
Reports of homes being torched by anti-IS fighters have been frequent in the course of the offensive.
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Such allegations are generally denied by commanders on the ground, who say the fires were set off by fleeing jihadists or used by their men as a way of detonating IS booby traps.
A top commander of the Popular Mobilisation units, paramilitary forces dominated by Iran-backed militias, admitted not all abuses could be prevented and deflected responsibility.
"As you know, there are internal conflicts between tribes and there are gangs but do you think the Popular Mobilisation did that?" Abu Mahdi al-Mohandis told reporters when asked about cases of property destruction.
"We cannot control everyone and put a guard in front of every home," he said, adding his forces had set up checks south of Tikrit to arrest looters and fighters guilty of other abuses.
It is still early to assess the discipline of Iraqi forces in reconquered areas only two days after IS lost Tikrit, and with the potential that a handful of trapped jihadists and the bombs they planted across the city still pose a threat.
- Calls for restraint -
Yet analysts argued the government camp appears to have at least partially succeeded in containing a widespread desire for revenge among Shiite fighters.
"The government and the religious authorities in Najaf took this issue very seriously," said Zaid al-Ali, author of "The Struggle For Iraq's Future".
"They issued a number of warnings and also dispatched hundreds of preachers to the front to remind fighters not to engage in looting, collective punishment or other forms of criminal activity."
Fanar Haddad, author of "Sectarianism in Iraq: Antagonistic Visions of Unity", agreed the operation could have gone much worse.
"While excesses have been committed and there may have even been instances of war crimes, we have yet to see evidence of what was widely feared: a systematic and pre-planned eradication of Tikrit," said Haddad, a research fellow at the Middle East Institute.
The US-led coalition, whose aircraft played a key role in breaking the back of IS resistance in Tikrit, said calls for restraint and respect of the civilian population paid off.
"I think the Iraqi government and the security forces and all those under the command of the security forces know the importance and profile of the issue," a senior coalition military official told AFP earlier.
"It's been reinforced again and again down the chain of command, and our information is that that has been a success," the official said on condition of anonymity.