Al-Sadr was executed in 1980 by Saddam.
Hoda Abd al-Hamid, Al Jazeera's Iraq correspondent, said from Baghdad: "There is a mixed reaction here in Iraq.
"We have heard from the Association of Muslim Scholars, a Sunni association, that issued a statement condemning the execution, saying it's an execution carried out by the [Nuri] al-Maliki government for the Americans.
"We also heard from a group of Baathists. They've posted a statement on the internet pledging their support again to Saddam Hussein and nominating his vice-president, Izzat Ibrahim al-Duri, who is still on the run since the fall in 2003, as the new president of Iraq.
"This video is likely to widen the gap.
"Sunnis are going to say this is proof that the security services have been infiltrated by Shia militias, namely the al-Mahdi Army which is loyal to Muqtada al-Sadr. The Sunnis have been saying that all along.
"The Shia will say he was not much ill-treated and that Saddam inflicted far worse.
"But there is a clear message coming out of that video - that the al-Mahdi Army is there and in charge of anything that's happening in Iraq now."
Caught on camera
On the video, a guard is also heard saying: "God damn you."
"God damn you," replies Saddam.
Saddam appeared to smile at those taunting him from below the gallows. He said they were not showing manhood.
Then Saddam began reciting the Shahada, a Muslim prayer that says there is no God but God and Muhammad is his messenger, according to an unabridged copy of the video clip, which was posted on a website.
Saddam made it to midway through his second recitation of the verse. His last word was Muhammad. Then the floor dropped out of the gallows.
'Act of revenge'
Najib al-Nuaimi, a member of the defence team, told Al Jazeera on Sunday that no Sunni lawyer was allowed to be among the execution witnesses and that the conduct of those present showed it was an act of revenge and for political purposes.
"This is not in the normal procedures to execute a normal person," he said.
"It's full of hatred and it's very ugly. It's nothing to do with the Dujail case."
By several accounts, Saddam was calm but scornful of his captors, engaging in a give-and-take with the crowd gathered to watch him die and insisting he was Iraq's saviour, not its tyrant and scourge.
Munir Haddad, an appeals court judge who witnessed the hanging, told the BBC: "He said we are going to heaven and our enemies will rot in hell and he also called for forgiveness and love among Iraqis but also stressed that the Iraqis should fight the Americans and the Persians."
Another witness, Mowaffak al-Rubaie, the Iraqi national security adviser, told The New York Times that one of the guards shouted at Saddam: "You have destroyed us. You have killed us. You have made us live in destitution."
Al-Rubaie told the newspaper that Saddam responded: "I have saved you from destitution and misery and destroyed your enemies, the Persians and Americans."