Tamim has a mixed population of Arabs, Kurds and Turkomen, with the oil-rich city of Kirkuk as its capital. Three American soldiers were killed last Wednesday by gunfire in Tamim.
Brig. Sarhat Qadir, a senior officer in the Kirkuk police department, said the bomber targeted a U.S. patrol base in a mostly Sunni Arab residential area in Rashad, about 25 miles southwest of Kirkuk.
The suicide attacker rammed his vehicle into blast walls outside the gates of the small U.S. base, located in a residential neighborhood of Sunni Arabs, Qadir said. He added that the explosives were concealed under tanned animal hides.
Earlier, the U.S. military issued a statement saying an American soldier died late Saturday when his vehicle was struck by a roadside bomb in eastern Baghdad.
At least 4,094 members of the U.S. military have died in the Iraq war since it began in March 2003, according to an Associated Press count.
In Baghdad, four police recruits were killed in a blast at the National Police headquarters, authorities said.
Another 22 people were wounded near the building's gate where recruits were gathering, they said. Police gave conflicting reports about whether the attack used mortars or a roadside bomb.
A mortar shell landed just outside Baghdad's Green Zone on Sunday, killing three civilians and wounding seven others, police said. The mortar was apparently targeting the Defense Ministry, which is inside the U.S.-guarded diplomatic zone, but fell short, they said.
Mortar and rocket attacks were once a daily occurrence in the Green Zone in central Baghdad, but have fallen off in recent weeks.
Another civilian was killed by a roadside bomb Sunday in northern Baghdad, police said. Five others were wounded in the attack, which took place about 100 yards from the Turkish Embassy. The target was believed to be a passing police patrol and not the embassy building.
Meanwhile, six shepherds were killed execution-style before dawn Sunday by suspected militants linked to al-Qaida masquerading as fellow herders east of Baghdad, police said.
The killings took place in a sprawling desert area where such militants are believed to have sought refuge after U.S.-Iraqi offensives against them in western Anbar province and in Baghdad, police said.
In Basra, Shiite extremists fired 10 rockets Sunday morning at the British base at the city's airport in the first attack there in nearly a month. No casualties were reported, but the attack raised concern that Shiite militias were trying to regroup after U.S. and British-backed Iraqi forces gained control of the city from extremists.
The U.S. command also announced that American soldiers in Baghdad captured an Iraqi arms dealer and "assassination squad" leader responsible for trafficking Shiite extremists in and out of neighboring Iran for training.
The arrest followed long-standing U.S. allegations that Iran arms, trains and funds Shiite Muslim militiamen inside Iraq - charges that Tehran denies. The arrest also coincided with a two-day visit to Iran by Iraqi Prime Minister Nouri al-Maliki, his second such trip in a year.
The Iraqi prime minister, himself a Shiite, is struggling to keep Washington happy while reassuring Iran, the largest Shiite nation, that a proposed U.S.-Iraqi security agreement would not make his country an American launching pad for attacks on Iran.
U.S. arrests against Shiite militiamen with alleged ties to Iran was likely to be on the agenda for al-Maliki's talks with Iranian officials.
U.S. soldiers, acting on intelligence from other Shiite militiamen already in custody, captured the Basra-based "special groups" leader late Saturday at a hideout in eastern Baghdad, according to a military statement.
"The wanted man is alleged to be a commander of an assassination squad in Basra, an arms dealer with connections to Iran and a document counterfeiter," the statement said.
He also arranges transportation of criminals into Iran for training, and then back into Iraq, it said. One of the leader's aides was also arrested without incident.
The U.S. military uses the term "special groups" to describe Shiite fighters defying a cease-fire order from anti-American cleric Muqtada al-Sadr, whose militiamen fought American and Iraqi forces for seven weeks until a May truce.
The military said in another statement that it captured six more suspected Sunni extremists Sunday in the northern city of Mosul, including an alleged al-Qaida in Iraq leader and another man who is a wiring expert in charge of a bombing cell there.
Two women were injured when American soldiers "breached the door of a target building" during the arrest raid, the statement said. Both were treated at the scene and then transported to an Iraqi hospital, it said.
Mosul is believed to be one of the last urban strongholds of al-Qaida in Iraq, and U.S. and Iraqi forces have battled with militants there in recent months.