Al-Baghdadi, about 85 km (50 miles) northwest of Ramadi in Anbar province, has been besieged for months by the radical Sunni Islamist militants who captured vast swathes of northern and western Iraq last year.
Militants attacked al-Baghdadi from two directions earlier in the day and then advanced on the town, intelligence sources and officials in the Jazeera and Badiya operations commands said.
The officials said another group of insurgents then attacked the heavily-guarded Ain al-Asad air base five km southwest of the town, but were unable to break into it.
About 320 U.S. Marines are training members of the Iraqi 7th Division at the base, which has been struck by mortar fire on at least one previous occasion since December.
Pentagon spokeswoman Navy Commander Elissa Smith confirmed there was “heavy fighting” in al-Baghdadi.
She said there had been no direct attack on the air base, but added: “There were reports of ineffective indirect fire in the vicinity of the base.”
An Iraqi defense ministry spokesman declined to comment on the situation in Anbar.
District manager Naji Arak confirmed that Islamic State insurgents had entered al-Baghdadia and attacked some government buildings.
He initially estimated the militants had taken 90 percent of the town but later said he could not confirm the extent of the group’s control as intermittent clashes continued into the early morning.
The death toll from the fighting was not immediately clear.
Most of the surrounding towns in Anbar fell under Islamic State control after the group’s rapid advance across the Syrian border last summer.
Elsewhere in Iraq, five civilians were killed when bombs went off in two towns south of Baghdad, police and medical sources said. Such attacks are not uncommon in and around the capital. (Reuters)