Earlier reports from Iraq suggested the hanging could take place today, but now some officials say privately it could be postponed to January 7.
On Death Row
The two officials are Hussein's half-brother, Barzan Ibrahim al-Tikriti, who headed Hussein's intelligence service, and Awad al-Bandar, the former head of the Revolutionary Court.
Both men were sentenced to death along with Hussein on November 5 for crimes against humanity in connection with the revenge killings of 148 Shi'ite civilians from Al-Dujayl following an assassination attempt on Hussein in 1982.
But when the two former officials will be executed remains uncertain.
Earlier, officials in Baghdad had told media privately that the hanging would be today. But as dawn -- the usual time for executions -- passed, some officials told news agencies the event was postponed to January 7.
The uncertainty comes as Hussein's execution continues to stir much international debate.
UN High Commissioner for Human Rights Louise Arbour appealed to Baghdad on January 3 not to hang Hussein's aides.
Fair Trial? Fair Process?
That repeats appeals from many human rights groups not to execute those sentenced to death in the Al-Dujayl trial:
"Human Rights Watch is against the implementation of the death penalty in general but particularly in this case of Saddam and his two colleagues who were on trial for the Dujayl massacrem," Human Rights Watch spokesperson Umri Shah told RFE/RL today. "We had many concerns over how the trial progressed and the many flaws in the whole process and, given that situation, the death penalty was totally inappropriate in this case."
The Baghdad government and Washington have said the Al-Dujayl trial process was fair and say Iraq's legal system has the right to apply capital punishment.
The debate over Hussein's execution has seen a number of world leaders present their views on capital punishment in recent days.
Sometimes, that itself has created further controversy.
UN Secretary-General Ban Ki Moon was asked for his view on Hussein's execution.
"The issue of capital punishment is for each and every [UN] member state to decide," Ban said. "As secretary-general, at the same time, while I am firmly against impunity, I also hope that members of the international community should pay due regard to all aspects of international humanitarian laws."
Ban -- who is from South Korea, a state with the death penalty -- was speaking on January 2 in New York. His remark stirred controversy because the UN Charter calls for the abolition of capital punishment.
Meanwhile, Italy has announced it will lead a drive in the UN to get a worldwide moratorium on executions.
The emotions over Hussein's hanging have risen with the circulation of an illicit mobile-phone video that shows witnesses in the gallows chamber taunting him before his death.
Prior to the video's appearance, the Iraqi government had portrayed the execution as a calm and dignified event:
"I am honestly proud of the way it was executed," Iraqi national security adviser Muwaffaq al-Rubay'i told CNN on December 30. "It was done in a proper way, in all the international standards and the Islamic standards and Iraqi standards. I am really, really proud of the way it went on."
The Iraqi government has since called for an investigation into the illicit videotaping of the hanging. But the government has given no sign it will call off its plans to execute Hussein's codefendants.
Saddam Hussein: Looking Back
MORE: A timeline of the life of Saddam Hussein.