But the mobile phone video showed the deposed leader being taunted in his final moments, with witnesses shouting "go to hell" before he dropped through the gallows floor.
The scene aired on Al Jazeera television was posted on the internet, prompting a worldwide outcry and protests.
Al-Maliki ordered his interior ministry to investigate who made the video and how it reached television and websites for public viewing.
"They used mobile phone cameras. I do not know their names, but I would remember their faces"
Munqith al-Faroon, an Iraqi prosecutor
An earlier US newspaper report said that Munqith al-Faroon, an Iraqi prosecutor who was present at the execution, identified the culprit.
"One of two men seen holding a cell phone camera aloft to make a video of Mr Hussein's last moments ... was Mowaffak al-Rubaie, Mr Maliki's national security adviser," he was alleged as saying.
On Wednesday however, al-Faroon denied reports that he had accused the country's national security adviser of being responsible for leaking the video.
"I am not accusing Mowaffak al-Rubaie [the national security adviser], and I did not see him taking pictures," al-Faroon said.
"I saw two of the government officials who were ... present during the execution taking all the video of the execution, using the lights that were there for the official taping of the execution.
|The video spread rapidly across the globe|
"They used mobile phone cameras. I do not know their names, but I would remember their faces."
The prosecutor said the two officials were openly taking video pictures, which are believed to be those which appeared within hours of Saddam's execution shortly before dawn on Saturday.
Al-Faroon said there were 14 Iraqi officials, including himself and another prosecutor, as well as three hangmen present for the execution.
All the officials were flown by US helicopter to the former military intelligence facility where Saddam was put to death in an execution chamber used by his own security men for years.
The prosecutor said he believed all mobile phones had been confiscated before the flight and that some of the officials' bodyguards, who arrived by car, had smuggled the camera phones to the two officials he had seen taking the video pictures.