After a major push on Tuesday that broke IS defences around the city centre, government forces have been slowed by snipers, booby traps, roadside bombs and suicide attackers.
While initial hopes of a quick victory have faded, Iraq's elite counter-terrorism service (CTS) and the army have advanced steadily through the devastated capital of Anbar province.
They reached a key intersection in the Hoz neighbourhood home to the government complex, whose recapture would go a long way towards ensuring a full recapture of Ramadi.
He said the latest fighting had left at least two members of the Iraqi security forces dead and nine wounded.
At least three were killed yesterday, according to several senior officers and local officials.
The figures they provide for IS casualties are high, with at least 23 killed yesterday alone.
The number of IS fighters hunkered down in central Ramadi was estimated at the start of the operation five days ago at no more than 400.
"CTS have made more progress, they're several hundred metres (yards) closer to the government complex," Warren said.
The advance by the government forces has also been hampered by the possible presence of dozens of families trapped in the combat zone and used by IS as human shields.
Government forces held off months of IS assaults in Ramadi until May 2015, when the jihadists blitzed their opponents with massive suicide car bombs and seized full control of the city.