Ammar al-Hakim also holds positions in SCIRI.
In February, US troops detained Ammar al-Hakim for several hours near the Iranian border, sparking protests in Shia cities. He was later freed.
Meanwhile, US soldiers were building a five kilometre-long wall to protect a Sunni enclave, Adhamiya, which is surrounded by Shia neighbourhoods and "trapped in a spiral of sectarian violence and retaliation," the military said.
Work on the cement wall at Adhamiya began on April 10, a mainly Sunni Arab area surrounded on three sides by Shia communities.
"The wall is one of the centrepieces of a new strategy by coalition and Iraqi forces to break the cycle of sectarian violence," Sergeant Mike Pryor, a public affairs officer, wrote in an article released by the US military.
Adhamiya is on the east bank of the Tigris River. Eastern Baghdad is predominantly Shia although there are some Sunni areas such as the nearby Fadhil district, a Sunni stronghold.
In a Friday sermon given to Shia worshippers in Kufa, 160km south of Baghdad, Mohammed al-Mohamadawi, a sheikh loyal to Muqtada al-Sadr, condemned US forces in Iraq.
"The chances of success [in Iraq] are essentially zero because the Iraqi people have no voice"
Non Sequitur, Cadiz, Spain
Send us your views"American forces are conducting an offensive on a mosque in al-Baiyaa, and worshippers are falling. Let the government see what the occupiers are doing to our people."
In an attempt to reduce car bombs on Fridays, vehicle bans were imposed on Baghdad and the northern cities of Tal Afar and Mosul, the authorities said.
The ban in Tal Afar began early on Friday and would be in place until further notice, police commander Ibrahim al-Jibouri said.
Intelligence reports indicated car bomb attacks were being planned in the area, he said.
A similar ban in Mosul, effective from the night before, remained in place on Friday.
In other violence, police said a roadside bomb killed one civilian and wounded three others southeast of Baghdad.
A rocket attack on a US military base killed one soldier and wounded two others, the military said on Friday.
The projectile struck a forward operating base in the town of Mahmudiyah, south of Baghdad, on Thursday night.
The death took the US military's losses in Iraq to 54 for this month alone and to 3,314 since the March 2003 invasion, according to an Associated French Press count based on Pentagon figures.
Clashes erupted between armed men and US and Iraqi forces around a Shia mosque in western Baghdad just before Friday prayers, witnesses and local media said. The US military said it was looking into the reports.
One witness said American helicopter fired on the mosque in Baiyaa, a religiously mixed neighbourhood in western Baghdad, just before noon.
"We were unarmed worshippers heading to the mosque for Friday prayers, and American Apache [helicopters] and tanks bombed the mosque and opened fire on worshippers," said Basim Abu Ali, who lives nearby.