Al-Dulaimi said that police were going from house to house with photos of the fugitives on Friday morning.
“The people of this city will help us bring them back to justice,” he said.
Police imposed a curfew on the city which lies 100km west of Baghdad, the capital.
The breakout attempt is said to have begun at 2am (23:00GMT), when the suspects killed a policeman and stole his weapon, before clashing with other members of staff.
Ramadi is a predominately Sunni city which was an al-Qaeda bulwark after the 2003 US-led invasion of Iraq.
However, since 2006 Sunni tribes in the area have sided with the US military and al-Qaeda fighters pushed out of the region.