Iraqi government employees returned to work under tight security in Ramadi on Sunday, but militants still held parts of the Anbar provincial capital and all of another nearby city.
Armoured vehicles and tanks were deployed at intersections in Ramadi, an AFP journalist reported, while a police officer said militants controlled two areas in the city as a crisis in Anbar province entered its 14th day.
Gunmen also hold Fallujah, another Anbar city and former insurgent stronghold located 60 kilometres (37 miles) from Baghdad.
It is the first time militants have exercised such open control in major cities since the insurgency that followed the 2003 US-led invasion.
Anbar governor Ahmed Khalaf al-Dulaimi had called for government employees to return to work on Sunday, the first day of the work week in much of the Arab world.
Many civil servants had stopped working days ago due to clashes and the presence of militants in the city.
Also on Sunday, security forces battled militants in Albubali, a stronghold of Al-Qaeda-linked fighters between Ramadi and Fallujah, a policeman in the area said.
And Sabah Noori, the spokesman for Iraq's Counter-Terrorism Service, said that some of its members were missing in the area.
On Saturday, Fallujah residents who had fled the city began to return after the fighting died down, and most businesses had reopened.
But tribal leaders said a combination of anti-government tribesmen and fighters loyal to the Al-Qaeda-linked Islamic State of Iraq and the Levant (ISIL) still held the city.
Washington has piled pressure on Baghdad to focus on political reconciliation, in addition to ongoing military operations.
The UN Security Council has voiced support for the government campaign to retake the two cities, while concern mounted over the battle for Anbar.
It urged "Iraqi tribes, local leaders, and Iraqi security forces in Anbar province, to continue, expand and strengthen their cooperation against violence and terror, and it stresses the critical importance of continued national dialogue and unity."
And Prime Minister Nuri al-Maliki called for Iraqis to back the security forces in their fight against militants, saying that "it is up to us to stand on the side of our armed forces and our security services".
On Friday, tribesmen and police retook two areas of Ramadi from Al-Qaeda-linked militants, tribal military commander Mohammed Khamis Abu Risha told AFP.
ISIL has been active in the Anbar fighting, but so have anti-government tribesmen.
At the same time, security forces have recruited their own tribal allies in the fighting that has raged in Anbar.
The army has for the most part stayed outside of Fallujah during the crisis, with analysts warning that any assault on the city would likely cause significant civilian casualties.
"The Iraqi army does not have the sort of precision weapons, intelligence and fire discipline to assault Fallujah without causing civilian casualties," said Jessica Lewis, a former US army intelligence officer who is now research director at the Institute for the Study of War.
In an assault, "the Iraqi security forces will most likely level Fallujah by overusing artillery and stand-off weapons."
The latest crisis comes ahead of national elections in April and, along with a months-long surge in violence countrywide, are among the biggest challenges to face Prime Minister Nuri al-Maliki during his eight years in office.
The Iraqi Red Crescent said it had provided humanitarian assistance to more than 8,000 families across Anbar but that upwards of 13,000 had fled Fallujah, while the UN special envoy has warned of a dire humanitarian situation.
A senior US official has said the crisis could take weeks to resolve.
Fighting erupted in the Ramadi area on December 30, when security forces cleared a year-old Sunni Arab protest camp.
The violence spread to Fallujah, and militants moved in and seized the city and parts of Ramadi after security forces withdrew.
Meanwhile, a car bomb targeted Iraqi army recruits in Baghdad on Sunday, killing at least eight people and wounding 12. The attack followed another that hit army recruits on Thursday, killing 23 people.