From the south, troops led by the counter-terrorism agency made progress in the Dubbat and Aramil neighborhoods, less than 2 miles from the city centre - where up to 300 militants are believed to be entrenched, General Ismail al-Mahallawi, the head of operations in Anbar province, told AP.
Sporadic clashes broke out and Iraqi forces on the advance were forced to remove roadside bombs planted by the extremists, al-Numani added.
Dubbat saw heavy fighting, with one soldier killed and 14 wounded, said an official in the Anbar operations room, speaking anonymously because he was not authorized to brief the media.
Al-Numani said no paramilitary forces — a reference to pro-government Shiite militias whose actions have raised concerns in Sunni territory — were taking part in the operation.
The Iraqi air force and the U.S.-led international coalition were providing air support to troops on ground and bombing IS targets, he said.
Fighting back: The Iraqi air force and the U.S.-led international coalition were providing air support to troops on the ground and bombing ISIS targets, counter-terrrorism units' spokesman Sabah al-Numani said
Destroyed: This photo, taken yesterday, shows a bridge destroyed by ISIS to block Iraqi security forces from moving forward on the Euphrates river, in northern Ramadi, which was taken by the jihadist group in May
Iraq's operation to recapture Ramadi - situated around 70 miles west of Baghdad - started in early November after a months-long effort to cut off supply lines to the city.
Progress has been slow because the government wants to rely entirely on its own troops and not use Shiite militias in order to avoid rights abuses such as occurred after the recapture of the city of Tikrit from the militants in April.
U.S. officials have also cautioned against the use of Iran-backed Shi'ite militias in retaking Ramadi from the hardline Sunni militants to avoid fanning sectarian tensions
Our forces are advancing toward the government complex in the centre of Ramadi. The fighting is in the neighbourhoods around the complex, with support from the air force.
Sabah al-Numani, Iraq's counter-terrrorism units' spokesman
Since overrunning Ramadi, ISIS has destroyed all the bridges around the city. It has also demolished the Anbar operations command and fanned out into the city's residential areas to set up less conspicuous centers of command.
As the military operation continues, Ramadi's civilian population — estimated to be between 4,000 and 10,000 — remains mostly trapped inside the city.
Iraqi officials say they believe civilians will be able to flee the city, but coalition officials report that so far they have only witnessed small groups doing so.
Ramadi, like the rest of Anbar province, is overwhelmingly Sunni Muslim, the minority community that complains of discrimination by the Shiite-led government in Baghdad.
Some Sunnis in other parts of Anbar and in northern Iraq welcomed IS rule, at least initially.
Retaking Ramadi would provide a major psychological boost to Iraqi security forces after Islamic State seized a third of Iraq, a major OPEC oil producer and U.S ally, last year.
Reclaimed: Today's military operation comes as the U.S.-led coalition has staged a fresh round of strikes against ISIS, with 17 in Iraq and eight in Syria. Above, an apparent US airstrike on Ramadi on November 21
Today's military operation comes as the U.S.-led coalition has staged a fresh round of strikes against ISIS, with 17 in Iraq and eight in Syria, the Combined Joint Task Force said in a statement.
The strikes near five Iraqi cities yesterday included seven near the northern Iraqi city of Mosul, which hit six tactical units and 12 fighting positions, according to the statement released today.
Six strikes near Ramadi hit two units as well as four weapons caches and two of the militant group's buildings, the task force leading the operations said.
In Syria, four strikes near Mar'a hit four Islamic State tactical units and a vehicle, the military said.
Other strikes near the Islamic State stronghold of Raqqa, al Hasakah and al Hawl struck three tactical units, among other targets, it said.