The militant push to take the capital of Anbar province comes two days before a planned parliamentary session to revive flagging efforts to replace the caretaker government in power since April elections.
Sunni militants have captured areas west of Ramadi since the fighting began yesterday afternoon, killing 11 police, bombing a police station and capturing another, an officer and a doctor said.
The officer, a police lieutenant colonel, said the insurgents were attempting to "storm Ramadi from the western side".
It could increase the threat to the capital by solidifying militant positions in Anbar and breaking the isolation of insurgent-held Fallujah, which lies only 60 kilometres west of Baghdad.
As the battle for Ramadi raged, Iraq's autonomous Kurdish region claimed control of several disputed northern oilfields.
"Members of the Kurdistan Regional Government and Kirkuk Oil Protection Forces moved to secure the oilfields of Bai Hassan and the Makhmour area," the region's government said.
The move enraged the Baghdad government, which labelled it "irresponsible behaviour which violates the constitution and the national wealth, and disregards the federal authorities and threatens national unity."
The oilfield seizures come after Kurdish peshmerga fighters moved into stretches of disputed northern areas vacated by Iraqi forces during the initial militant offensive last month, and regional president Massud Barzani has said they will stay there.
