Aljazeera has learned that the clashes erupted after the fighters, armed with rocket-propelled grenades (RPGs) and machine guns, attacked al-Wihda police station in the centre of the city, early on Sunday.
Columns of smoke have been seen rising from the area as clashes continue across the city.
Other reports state that two police officers and a woman were injured.
Also on Sunday, two US soldiers were injured when a car bomb exploded next to their convoy on the road leading to Baghdad airport, a military statement said.
It said the vehicle-borne improvised explosive device damaged one of the vehicles in the convoy, and that after the blast patrols closed the road to clear it of debris.
The two soldiers were evacuated to a nearby military hospital, the press release said.
Ball of fire
Fadil Jawad, a local resident who said he watched the attack from the roof of his home, described a late-model luxury car overtaking the six-vehicle convoy moments before exploding in a ball of fire.
Two of the Humvees in the convoy were destroyed by the blast and the rest scattered off the road, he said. Two Black Hawk helicopters arrived and evacuated wounded soldiers, Jawad said.
Military convoys and combat
patrols are regularly targeted
The military statement said there were no reported civilian casualties.
But the interim government's youth ministry reported that its general director, Ahmad Faiq, and his bodyguard were injured when their car was hit by the explosion.
The highway leading from downtown to the international airport is considered one of the most dangerous stretches of road in Iraq for US troops.
Military convoys and combat patrols are regularly targeted on the busy thoroughfare, which cuts through central Baghdad.
On Saturday, a bomb detonated near two armoured buses on the same road, damaging both, but causing no casualties.
Elsewhere, a US military tank was destroyed when it was hit by an explosive device in al-Dhuluaiya district south of Tikrit, Aljazeera has learned.
Casualties among US soldiers are not yet known.
Also on Sunday, a US military base came under RPG attack in the Sailu district, northwest of Samarra city.