Iraqi Premier Haider al-Abadi has vowed to recapture the city, Anbar's provincial capital, within days.
The volunteer forces, supported by a smaller group of government troops, advanced Tuesday to within a few kilometers of a university on Ramadi's southwestern edge, police sources and tribal fighters allied to the government said.
As they passed through farmland south of Ramadi, the militiamen told people to return home and stay inside, promising they would not be harmed.
"The Labaik Ya Hussein operation is led by the Popular Mobilization forces in cooperation and coordination with the armed forces there," a spokesman for the volunteer forces, Ahmad al-Assadi, told a news conference.
"We believe that liberating Ramadi will not take long," he was quoted by Reuters as saying.
Ramadi fell to the ISIL militants on May 17 in a serious setback for Iraqi forces, which has also cast doubt on the effectiveness of the US strategy of air strikes to help Baghdad roll back the insurgents.
Ramadi, situated about 110km west of Baghdad, is the capital of Anbar province. The strategic city extends along the Euphrates River and is the largest city in the governorate.