Elsewhere, six coalition soldiers — two Poles, three Slovaks and a Latvian — were killed in an explosion while defusing mines in Suwayrah, 25 miles south of Baghdad, authorities said.
One of the car bombs blew up as a convoy of provincial council members passed by in the northern city of Mosul. The council members escaped injury, officials said. Nine people died and about 25 were injured, the U.S. military said.
In the other attack, a suicide attacker detonated a car bomb during rush hour outside the American base in Baqouba, about 30 miles northeast of Baghdad.
At least five Iraqis and one American soldier were killed, the U.S. military and police said. Fifteen Iraqis and 10 American soldiers were wounded.
In Ramadi, eight Iraqis were killed and three injured in a bombing, while a mortar attack in Mosul injured two contract employees.
A U.S. Marine was also killed in action on Monday in Anbar province west of Baghdad, but the military released no further details.
In other developments:
Violence continues against U.S. forces and their allies in the countdown to the handover of sovereignty in Iraq on June 30. A car bomb exploded Sunday near the gate of another a U.S.-run base north of Baghdad, killing nine people and injuring 30 others — including two American soldiers.
The new Iraqi interim government has made security its top priority as it assumes more responsibility for running the country. The new prime minister, Iyad Allawi, is close to the CIA and the State Department and as an exile leader headed an opposition group made up largely of former military officers who had broken with Saddam Hussein.
In an effort to improve security, Allawi announced an agreement Monday by nine political parties to dissolve their militias, integrating some of their 102,000 fighters into the army and police and pensioning off the rest.
The plan does not cover the most important militia fighting coalition forces — the al-Mahdi Army of radical cleric Muqtada al-Sadr — or smaller groups that have sprouted across the country since the collapse of Saddam Hussein's regime in April 2003.
Those groups will now be considered illegal.
The main groups affected by the agreement are Kurdish peshmerga militiamen who fought alongside American troops during the 2003 invasion that toppled Saddam. Most of the others had effectively dissolved already. The other main group still active is the Badr Brigade of the Supreme Council for the Islamic Revolution in Iraq, a mainstream Shiite party.
U.S. officials want to disband the al-Mahdi Army and arrest al-Sadr for the April 2003 murder of a rival cleric, although authorities have deferred both goals to reduce tensions in the Shiite heartland south of Baghdad. Instead, the coalition has opted to let Allawi, himself a Shiite, and Shiite clerics deal with al-Sadr.
Meanwhile, a spokesman for former Governing Council Member Ahmad Chalabi demanded that Jordan open a new investigation in fraud charges that led to Chalabi's 1991 conviction in absentia in a banking scandal.
Chalabi's spokesman, Mithal al-Alusi, said the head of the Iraqi National Congress party was unfairly tried by a military court and that Chalabi can prove his innocence before a civilian panel.