Fighting raged around the former government headquarters in Ramadi, a key position whose recapture by federal forces would mark another key step toward reclaiming the city they lost to the Islamic State group in May.
"The Iraqi forces are in Hoz neighbourhood... About 500 metres (yards) away from the governmental complex," an army lieutenant-colonel told AFP from Anbar province.
"They are advancing very cautiously" in the southern neighbourhood of Hoz, said Sabah Karhout, the head of Anbar provincial council.
"There's stiff resistance, there's been fierce fighting over the last 24 hours in the southern part of Ramadi city," said the US-led coalition's spokesman, Colonel Steve Warren.
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"They've established a strong defence using improvised explosive devices as mine fields, booby traps, rigging entire houses to explode," he said.
IS had positioned around 100 fighters along the main approach to the government complex, he added.
"Because of the restrictive nature of the terrain, it's difficult to mass combat power. It's easy for a small number of people to hold a large number of people off," he said.
And 22 wounded soldiers were brought in early on Thursday, said a medic at Abu Ghraib hospital, west of Baghdad.
Statements issued by IS spoke of higher casualties among government forces, including in an attack it said carried out with five suicide bombers early Thursday west of Ramadi.
"Three of them advanced towards the main entrance... And managed, thanks to God, to kill all the guards with silenced weapons," the statement said.
"The other two entered by the back door and managed to kill several others and set fire to the armoury," it said.
Ibrahim al-Osej, a Ramadi councillor, said the number of IS fighters left in Ramadi was estimated to be "smaller than a battalion," or fewer than 400.