Sunni militants on Friday advanced into new areas of Ramadi after early morning clashes in the city centre and deployed snipers on one street, according to a foreign news agency.
There were conflicting reports about the fighting in Fallujah.
Quoting a policeman, the news agency report said that while about a quarter of the city remained under the control of the Al-Qaeda, the army had re-entered several areas. However, a colleague said the army had yet to enter the city.
There has been fierce fighting in recent days as government forces have tried to force militants aligned to the Islamic State of Iraq and the Levant (ISIS) out of Ramadi and Fallujah.
There has been a surge in sectarian violence in Iraq since April, when there was a deadly crackdown on a Sunni protest camp in Hawija.
Extremist Sunni militants subsequently stepped up attacks across the country, while Shia groups began deadly reprisals.
On Wednesday, the United Nations said at least 7,818 civilians and 1,050 members of the security forces had been killed in 2013.
The annual death toll was the highest in years, but still significantly below those recoded at the height of the insurgency in 2006 and 2007.
