Meanwhile, investigators are trying to determine the veracity of a rumor that the video was sold for $20,000, reports CBS News correspondent Randall Pinkston.
National Security Adviser Mowaffak al-Rubaie laid the blame for the cell phone video on ill-educated security guards, saying "Their feelings were expressed in a wrong way, in an unacceptable way, in a disgusting way."
But one of the prosecutors from Saddam's trial disputes that, telling CBS News, "They are trying to blame the guards. The guards are innocent."
Al-Rubaie told CNN that the guard force at the execution was infiltrated by an Arab television station or another outsider.
The clandestine and leaked footage appeared on Al-Jazeera satellite television and Web sites just hours after Saddam was hanged Saturday. The tumultuous scenes quickly overshadowed an official execution video, which was mute and showed none of the uproar among those on the floor of the chamber below the gallows.
The video, which ignited by Saddam's fellow Sunni Arabs in various Iraqi cities, has threatened to turn the ousted dictator into a martyr. Saddam was shown never bowing his head as he faced death, and asking his taunters if they were acting in a manly way.
In other developments in Iraq:
A U.S. military spokesman, Maj. Gen. William B. Caldwell, said Saddam was dignified and courteous to his American jailers up to the moment he was handed over to the Iraqis outside the execution chamber. He said no Americans were present for the hanging.
Sami al-Askeri, a Shiite lawmaker who advises al-Maliki, said two Justice Ministry guards were being questioned. "The investigation committee is interrogating the men. If it is found that any official was involved, he will face legal measures."
A second key al-Maliki adviser, who spoke on condition of anonymity because he was not authorized to release the information, said, "In the past few hours, the government has arrested the person who videotaped Saddam's execution. He was an official who supervised the execution and now he is under investigation."
Despite the report of only one arrest in the videotaping, prosecutor Munqith al-Faroon, one of 14 official witnesses to the execution, told The Associated Press that he saw two government officials using their camera phones.
"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," he said. "They used mobile phone cameras. I do not know their names, but I would remember their faces."
Caldwell said the tumultuous execution would have gone differently had the Americans been in charge.
As the storm over the handling of the hanging gained strength, Caldwell was among several U.S. officials who suggested displeasure with the conduct of the execution.
"If you are asking me: 'Would we have done things differently?' Yes, we would have. But that's not our decision. That's the government of Iraq's decision," Caldwell said.