In other developments, police found the bodies of 32 more death squad victims scattered around Baghdad on Thursday, bringing the two-day total to nearly 100, and a Sunni Muslim leader said the slayings could destroy the political process.
The same day, Iraqi soldiers raided an office run by supporters of Shia leader Moqtada al-Sadr, unleashing a chain of events that left two people dead, nine wounded and the city of Diwaniya under curfew.
US troops reinforced the Shia city, 180km south of Baghdad, two weeks ago after fighting between Sadr's Mahdi Army militia and the Iraqi army left dozens reported dead.
Also on Thursday, a roadside bomb killed six people and wounded 13 others in the city of Falluja in Iraq's western Anbar province, police said.
The alleged al-Qaeda in Iraq commander, Abu Jafar al-Liby, was killed during an operation in Baghdad three days ago, Brigadier Abdul-Karim Khalaf, interior ministry director of operations, told AP on Thursday.
Four others were killed and two others arrested during the raid, he said.
According to Khalaf, al-Liby was the head of "al-Qaeda's criminal operations" in Baghdad's al-Rasafa and al-Karrada districts and the province of Diyala, northeast of the capital.
Two letters were found with the body - one for Osama bin Laden and the other for Abu Ayub al-Masri who took over al-Qaeda in Iraq after Abu Musab al-Zarqawi was killed in an American air strike on June 7, Khalaf said.
The letters reportedly expressed his loyalty and promised more attacks.
A large quantity of explosives and a number of suicide vests were found during the raid on Sunday.
The second man - an associate of the group's new leader and head of assassination, kidnapping and bomb-making cells - was captured on Tuesday, Major-General William Caldwell, a US military spokesman, said.
"As part of these operations on Tuesday evening alone there was a series of 25 raids in and around Baghdad targeting al-Qaeda in Iraq activities. A key outcome of these raids was the capture of over 70 suspected terrorists, one of which was the personal associate of Abu Ayub al-Masri," Caldwell said.
The unnamed suspect "directly participated in numerous terrorist acts including kidnappings and executions, terrorist acts and others, contributing to sectarian violence throughout the city".
On Thursday, Adnan al-Dulaimi, leader of the Iraqi Accordance Front, parliament's biggest Sunni Arab group, said of the death squad murders: "If these barbaric acts do not stop, certainly it will affect the reconciliation plan."
In one incident, six members of a Shia family, including two women and a three-month-old boy, were shot dead in their home at a school where the father worked as a caretaker in a mainly Sunni district of west Baghdad.
The baby, Seif, lay wrapped in a bloodsoaked towel at a nearby hospital morgue, a bullet hole in the back of his neck.
The US military said that "66 terrorists have been killed and 830 suspected terrorists detained" in 150 operations since August 30.
Caldwell said there had been a "spike in violence in Baghdad over the last 24 hours" as Iraqi police found the bodies of 20 people who had been tortured and shot left around the capital.
Most of the bodies had their hands tied and were blindfolded, a security official said. Police recovered 64 bodies on Wednesday.
At least 15 more people died and dozens have been wounded in a series of car bombings and shootings across central Iraq.