"People are doing the same as (in) Saddam's time and worse," he was quoted as saying. "It is an appropriate comparison."
Allawi accused fellow Shia in the government of being responsible for death squads and secret torture centres.
"These were the precise reasons that we fought Saddam and now we are seeing the same thing," the newspaper quoted him as saying.
For months, Sunni Arabs have been accusing the Interior Ministry of wholesale arrests and abuse of Sunnis in an attempt to find a handful of armed fighters.
The discovery by US troops this month of up to 173 detainees - malnourished and some showing signs of torture - hidden in an Interior Ministry building in central Baghdad gave credence to those charges.
The Iraqi government has set up a committee that is investigating the case, but President Jalal Talabani told reporters on Sunday that he didn't think there was a serious problem.
Protesters demanded information
about detained relatives
"I believe there is exaggeration, but every incident should be investigated," he said.
In Baghdad on Sunday, a group of women protested outside the Ministry of Interior building, demanding information about relatives who have been taken by security forces, never to be heard from again.
"Let the government tell us where they are. If they were killed let them tell us where their bodies are," said one woman, who identified herself only as Um Nabeel.