"They are clearing several other neighbourhoods," he said.
Police chief Hadi Irzayij said security forces detained 30 suspected Islamic State group fighters "who were attempting to flee Ramadi by blending in with civilians."
"We are following a plan put together in a way that will prevent casualties in the ranks of the security forces," he police chief added.
IS, which took full control of Ramadi in May 2015, had planted thousands of explosive devices on roads and in buildings to defend the city.
Clearing operations are led by Iraq's elite counter-terrorism service (CTS), along with army, police and local tribal forces, as well as aerial backing from the US-led anti-IS coalition.
The jihadists are no longer in a position to fight back, but many managed to pull out of last week's main battle and redeploy in eastern Ramadi or nearby rural areas.
On Friday, IS staged a large attack on a compound used by the army's 10th Division, in a desert area north of Ramadi.
"They used six suicide vehicles followed by a commando of fighters wearing explosive belts," said a lieutenant colonel.
"They managed to take control of the base when the army had to pull out because it suffered casualties... Iraqi forces have since counter-attacked and retaken control, with aerial coalition backing," he said.
- Lack of food -
Coalition spokesman Colonel Steve Warren confirmed the attack and said he expected the Iraqi forces to soon retake full control of the compound.
A CTS colonel confirmed Friday that around 30 IS militants had been arrested as they tried to slip out of Ramadi, describing some of them as senior local leaders.
Majed Mohammed, a CTS major, told AFP: "What we are doing now is saving the trapped families".
He said their task was complicated by the high number of roadside bombs and the fact that IS was firing on civilians trying to escape.
One woman who was evacuated from an IS-held area on the eastern edge of Ramadi said the jihadists tried to round up residents when some of them started fleeing.
"We refused; we stayed in our houses and the word reached us that the Iraqi forces were coming," she said, refusing to give her name.
"We were 15 homes. We got in touch with each other and left all together at seven in the morning... They (IS) tried to stop us and chased us but the Iraqi forces arrived," she said.
Lieutenant General Abdul Ghani al-Assadi, the commander of CTS, told AFP 400 families were rescued and taken to safety by the security forces on Wednesday and Thursday alone.
"We take charge of the families according to a well-executed plan by our troops, and this plan guarantees the safety of those families," he said.
A police lieutenant colonel said another 90 people, including 73 women and children, were evacuated Friday from the Thayla neighbourhood.
"Our forces there also found seven bodies, including two women and two children, that appeared not to have any wounds," he said.
Temperatures have been low in recent days and civilian survivors have said the fighting had left them with little or no access to food.
Sitting in a tented camp in Habbaniyah where the army took most of the evacuated families, one woman recounted her family's survival.
"We had no food, no flour. We only had flour for animals. We had to pick out the bugs before kneading and eating it," she said.