Ramadi, the largest city retaken by government forces, was touted as the first major success for Iraq's army since it collapsed in the face of ISIS's lightning advance across the country's north and west 18 months ago.
But almost all the city remains off-limits to its residents, most of whom fled before the army advance, said security services.
"The security forces are advancing to a large degree inside Ramadi. Most areas are now under their control," Anbar governor Sohaib al-Rawi said on Saturday at a temporary government complex southeast of the city.
"Most of the streets in Ramadi are mined with explosives so it requires large efforts and expertise," he added.
The counter-terrorism forces which spearheaded the military campaign to retake the capital of western Anbar province are securing only main streets and buildings considered tactically important, security sources said.
They have built up earth banks at the entrance of central neighbourhoods deemed clear of militants but still laden with explosives, and marked many buildings' exteriors as "mined", the sources added.
The United Nations Development Programme is still waiting for the green light from the Iraqi government to enter the city and start work to rebuild it.