The bombings happened on Thursday, a day when three Jordanian truck-drivers were taken captive. Two local Iraqi leaders were gunned down elsewhere.
The US military said that a car sped towards the council building in Dujail, a city 50km from the Iraqi capital.
"It detonated in front of the building," said US military spokeswoman Cynthia Weasner, adding that there had been no US casualties.
Two of the dead were guards while the other two were municipal workers, said a police officer.
A second car laden with explosives exploded near a checkpoint in town of Iskandariya, south of Baghdad, on Thursday morning, wounding six national guards, a US military spokesman said.
Iraqi National Guardsmen were
hurt in the second attack
"The Iraqi National Guard was hit by a vehicle-borne improvised explosive device followed by small-arms fire," said the spokesman, adding that US marines ferried the casualties to a nearby base for treatment.
Public buildings are frequently targeted in fighting that has pitted fighters against the US-backed government and its security forces as well as US-led troops in Iraq.
In a separate attack northeast of the Iraqi capital, armed men opened fire on a car that was carrying a local village chief.
Jassem Ali, who heads the Heb Heb village, was fatally wounded and two bodyguards were hurt, one seriously, local police chief Mehdi Muhammad said.
Police in the northern city of Kirkuk, meanwhile, found the body of a man thought to have collaborated with US forces, police chief Turhan Yusif said.
Ramadi witnessed the killing of
a powerful local tribal chief
"It appears he was an Iraqi," he said, adding that the man had been blindfolded and shot.
In Ramadi, 100km west of Baghdad, Shaikh Khamis Futaikhan, head of the powerful local Abu Risha tribe, was shot dead in an ambush on his car, police said.
Meanwhile, a Jordanian man died of injuries sustained in an armed attack on Thursday by an Iraqi group that also captured three Jordanian truck drivers in the same convoy, an official at the Jordanian Truckers Association said.
Abd al-Rahim Jamal, the association's representative in northern Jordan, told Aljazeera: "We have contacted our foreign ministry which had got in touch with the Jordanian embassy in Baghdad asking that Jordanian drivers be given protection."
Jamal said a section of Iraqi drivers had collaborated with the captors to ensure that Jordanian drivers did not enter Iraq.
Earlier on Thursday, Aljazeera television broadcast a tape showing three men purported to be Jordanian truck drivers said to be held in Iraq by a previously unknown group, called Jaish al-Islam. The three were flanked by two masked armed men.
More than 170 foreigners, including nearly two dozen Jordanians have been seized in Iraq since Saddam Hussein's fall in April last year.