Iraqi rebels seized the centre of the city of Ramadi and attacked police stations elsewhere as US-led troops continued their Falluja assault.
Armed insurgents in Ramadi moved in when US troops withdrew from the Sunni city, a former rebel stronghold.
Iraqi police and national guard stations in Baquba, Kirkuk and Baghdad were also targeted - reports speak of a number of casualties.
The US military said it "associated" the attacks with the Falluja assault.
"The enemy is concentrating on Iraqi security forces " to intimidate them, US Lieutenant General Thomas Metz told reporters at a Pentagon briefing.
Show of force
In Ramadi, about 113km (70 miles) west of Baghdad, hundreds of armed insurgents massed to the heart of the city after US troops had withdrawn.
Rebels - who have recently been fighting US troops in the city - are reported to have been dancing and shooting into the air in a show of force, the BBC's Caroline Hawley in Iraq reports.
"The residents of Ramadi condemn the attack against Falluja and we appeal to the inhabitants of Ramadi to wage jihad [holy war] against the American occupants who want to eradicate Islam," one city resident was quoted as saying by the AFP news agency.
On Tuesday, rebels also targeted several police stations in and around Baquba, about 60km (40 miles) north of Baghdad, Iraqi officials said.
A number of police officers were injured in the attacks and at least one attacker killed, reports say.
In the oil-rich Kurdish town of Kirkuk - about 250km (155 miles) north of Baghdad - a suspected car bomb outside an Iraqi national guard based killed at least two people, officials said.
In a separate incident, a group of armed men attacked a police station in south-western Doura neighbourhood in Baghdad, police said.
A police source said he believed there were casualties, but gave no details, Reuters news agency reported.