A statement by the group posted on the Internet said the bomber Saturday came from Syria, bolstering long-standing U.S. claims that foreign fighters are involved in insurgent attacks in Iraq.
Fighting flared anew in the Shiite holy city of Najaf and nearby Kufa between American soldiers and the Shiite militia of anti-U.S. cleric Muqtada al-Sadr, with bursts of heavy mortar and machine gun fire heard about midnight. A live report on Al-Jazeera television from its correspondent in Najaf was punctuated by strong explosions near a downtown hotel.
Also Saturday, the military said a U.S. soldier was killed and three others from the U.S. Army's 1st Armored Division were wounded in an attack on their vehicle south of Baghdad, and a Marine died in a non-hostile incident.
It said the soldiers' vehicle was "ambushed by a vehicle-borne improvised explosive device" in Mahmoudiyah, 20 miles south of Baghdad. The statement did not say when the attack occurred.
The military said the Marine, assigned to the 1st Marine Expeditionary Force, died Friday near Camp Fallujah, west of Baghdad, while "conducting security and stability operations."
Saturday's suicide blast outside the home of Abdul-Jabbar Youssef al-Sheikhli, the deputy interior minister in charge of security, hurled two cars onto the front lawn of his house. Police fired warning shots to disperse distraught bystanders who scuffled with them after the attack.
Al-Sheikhli was injured in the forehead and right arm, said Hassan Hadi, a Health Ministry official.
Bodyguards fired on the bomber's car as it approached, said Brig. Gen. Mark Kimmitt, the chief U.S. military spokesman in Iraq. Three bodyguards and a woman were killed as well as the bomber, he said. Earlier, Iraqi authorities said four police died.
Al-Sheikhli belongs to the Shiite Muslim Dawa party, which lost a prominent member in another fatal car bombing on Monday. The president of the Iraqi Governing Council, Dawa member Izzadine Saleem, was killed along with at least six other people near the headquarters of the U.S.-run coalition in the capital.
The Monotheism and Jihad Group, which claimed responsibility for Saleem's death, said it carried out the attack Saturday as a warning to the United States and its allies.
"They will not be safe from the hand of God's retaliation, then the mujahedeen's, and that they should be ready," said the statement, posted on an Islamic Web site.
It said "martyr" Ahmed el-Shami Aby Abdel Rahman, from Qamishli, Syria, "drove a car bomb to take (al-Sheikhli) to hell."
The group's leader is believed to be Abu Musab al-Zarqawi, a Jordanian wanted by the United States for organizing al Qaeda operations in Iraq and suspected of.
In Najaf, south of Baghdad, fighting broke out Saturday between U.S. forces and al-Sadr's militia near the city's police directorate and the governor's office. At least 10 people were injured in the Saturday clashes, which erupted again about midnight, according to Radhi Kadhim, a nurse at al-Hakim Hospital.
Residents of Najaf reached by telephone said they could hear the sounds of automatic weapons fire and explosives late Saturday coming from Najaf's twin city, Kufa, but efforts to reach anyone there were unsuccessful.
On Friday, five people were killed and 29 injured in Kufa in clashes between al-Sadr's fighters and U.S. troops after the arrest of Mohammed al-Tabtabaei, an aide to the fiery cleric, a hospital employee said on condition of anonymity.
There was no combat in Karbala, another holy city where intense battles have occurred. Residents said there were no combatants on the streets, and al-Sadr's office said militiamen and U.S. forces had agreed to withdraw from the city.
Kimmitt said the coalition had repositioned some forces, but had not withdrawn. Early Friday, U.S. troops pulled out of a central mosque that they had occupied after ousting insurgents who had used it as a base.
"The police chief from Karbala in fact came to us the other day and said he was encouraged to start bringing back in Iraqi police into the city of Karbala," Kimmitt said.
Iraqi leaders in Karbala have been trying to negotiate an end to the fighting, though coalition officials have stood by their position that al-Sadr disband his militia and "face justice." The cleric, who launched an uprising against the coalition last month, is wanted in the murder of a rival moderate cleric last year.
Kimmitt said efforts to end fighting in Sadr City, an al-Sadr stronghold in Baghdad, had broken down because coalition forces continue to be attacked. Troops had temporarily suspended patrols to give tribal leaders time to negotiate with the militia.
Seven mortar rounds landed north of downtown Baghdad on Saturday, Kimmitt said. Two coalition soldiers and an Iraqi civilian were slightly injured.
In another area of Baghdad, a rocket struck a two-story house near the former Ministry of Information. There were no reports of casualties.