Without naming al-Lami, the U.S. military in Iraq said the suspect arrested Wednesday evening is believed to be a senior leader of "special groups" - Iranian-backed militiamen in Iraq.
Al-Lami's detention could also further discredit attempts by the Shiite-led government to keep top supporters of Saddam Hussein out of senior government jobs. Al-Lami was in charge of that task, as head of a committee that screens former Baath party members.
He and his family were returning to Baghdad from Lebanon, where he underwent medical treatment, when he was arrested at the city's international airport, said Qaiser Watout, a member of al-Lami's committee.
U.S. troops were waiting for al-Lami as the plane's doors opened, Watout said, adding that his family was allowed to proceed.
"We condemn this act," Watout said. "Al-Lami was a moderate official and we are surprised by his arrest."
The U.S. military confirmed it arrested a senior Shiite figure Wednesday, but would not release the name or say whether it was al-Lami. The military said the man, who was known to travel to Iran and Lebanon, was detained after his plane landed at the airport.
The U.S. military intelligence official in Iraq confirmed al-Lami's arrest. He said he has received several reports about al-Lami's alleged involvement in a June 24 bombing.
The official spoke on condition of anonymity because he is not authorized to discuss intelligence information with reporters. He said al-Lami is believed to have information that could lead U.S. officials to others.
The military said the detainee is believed to be behind the June attack that killed 10 people, including two U.S. soldiers and two American civilians, in a district council building in Baghdad's Shiite slum of Sadr City, the military said.
Iraqi officials have said it appeared to be an inside job and suspicion at the time fell on the headquarters' Shiite Muslim guard force.
The Iraqi Defense Ministry also said it appeared the Iraqi council members and not the Americans were the main target of the blast, which came ahead of an election to choose a new chairman of the council.
The bombing hit as the U.S. military and civilian officials were stepping up efforts to promote the local administration and restore services in Sadr City and other areas, amid a sharp drop in violence.
Meanwhile, anti-American Shiite cleric Muqtada al-Sadr released a statement saying his largely disbanded Mahdi Army militia would extend its cease-fire "until further notice."
The statement, which was read by an aide in the Iraqi holy city of Najaf, also warned that any "person who violates" the truce would no longer be considered part of the Mahdi Army.
Al-Sadr's militia battled U.S. and Iraqi forces for years, but last year he declared a cease-fire. The truce had been extended in six-month increments, but Thursday's statement indicated it would now be considered open-ended.
Last month, al-Sadr, who lives in Iran but retains significant clout in Iraq, announced he was transforming his militia into a social welfare body with a few guerrilla cells to attack U.S.
troops if Washington doesn't agree to leave Iraq. The announcement followed setbacks in battles with the U.S.-supported Iraqi army in Baghdad, Basra and Amarah.
Separately, the U.S. military said an American soldier died of wounds he received after coming under fire while patrolling northern Baghdad on Wednesday. Another U.S. soldier was killed in a roadside bomb attack while on patrol Thursday in Baghdad, the military said.
