Kurdish peshmerga forces also engaged in hours of heavy fighting in Kirkuk province in northern Iraq against IS, which spearheaded a major offensive in June that overran key parts of the country.
"We are defending and protecting the governmental complex" in Ramadi, said police Colonel Hamid Shandukh, adding militants were within a few hundred metres (yards) of the governor's office.
The fighting began when soldiers and police pulled back from Al-Hoz, an area that stretches from Ramadi's south to its centre, Shandukh said, adding the government complex area was now being defended by security forces and hundreds of tribesmen.
Another officer, Colonel Salah Arrak al-Alwani, also confirmed fighting in central Ramadi, and said it had been going on for nine hours.
"If we lose Anbar, that means we will lose Iraq," the province's governor, Ahmed al-Dulaimi, told Al-Anbar television from Germany, where he is recovering after being wounded by a mortar round in September.
"I will very soon be with the tribes and the security forces in Anbar to fight" the Islamic State group, Dulaimi said.
Parts of Ramadi and all of Fallujah, to its east, have been outside government control since the beginning of the year, but much more of the province has since been overrun by IS, prompting warnings it could fall completely.
Iraqi security forces wilted under the initial June IS onslaught, but are now backed by US-led air strikes, international advisers, Shiite militiamen and Sunni tribes, and have begun to claw back some areas.
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Kurdish peshmerga forces have also battled IS across a front stretching from the border with Syria to Iran, sometimes in concert with federal forces and other times alone.
On Wednesday, the peshmerga held off a major attack by IS forces in the oil-rich province of Kirkuk, officers said.
"They are targeting Kirkuk and they want to control the oil sites," said peshmerga Major General Westa Rasul.
The attack began early on Wednesday morning against three villages west of the city of Kirkuk, sparking fighting that lasted for hours, Rasul and two other officers said.
IS managed to seize one village, but Kurdish forces backed by air strikes later succeeded in retaking it.
One policeman and five peshmerga, including a colonel and the son of a Kurdish politician, were killed and 28 wounded in the fighting, officers and a doctor said.
When federal security forces crumbled under the weight of the June offensive, Iraq's autonomous Kurdish region took control of a swathe of disputed northern territory it wants to incorporate against Baghdad's wishes.
But IS turned its attention north in August, driving Kurdish troops back toward their regional capital Arbil and helping spark the US-led air campaign.
Backed by the strikes, Kurdish troops have regained territory from IS, but the group still holds parts of Kirkuk province and other northern areas.