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Barzan al-Tikriti, one of Saddam's half-brothers and his former intelligence chief, and Awad al-Bander, a former judge, were due to be hanged today, but the killings have been delayed.
A senior official from the Prime Minister Nouri al-Maliki's office, speaking on condition of anonymity, claimed the execution had been postponed "due to international pressure".
Bahaa al-Araji, a lawmaker for radical Shia cleric Moqtada al-Sadr's political group, said he believed the executions would be delayed until Sunday, the first working day after the Eid al-Adha holiday.
Calls for restraint have come from Ban Ki-moon, the new United Nations Secretary-General, and Louise Arbour, UN High Commissioner for Human Rights, who urged Iraq not to execute the men out of respect for international law.
Michele Montas, a UN spokeswoman, said: "The secretary general strongly believes in the wisdom of Article 3 of the Universal Declaration of Human Rights which states everyone has the right to life, liberty and security of person."
"He fully endorses the call made today by Louise Arbour for restraint by the government of Iraq in the execution of the death sentences imposed by the Iraqi high tribunal."
Mr al-Maliki has already signed the death warrants as part of an order authorising the execution of Saddam. He has come under pressure for the speed and timing of Saddam's execution on the first day of Eid.
In Iraq, thousands of Sunni Arabs have marched to vent anger at the execution and mourners have flocked to Saddam's grave in his home village of Awja.
The US military has expressed concerns over the manner in which Saddam was hanged and Britain has condemned the leaking of the video showing guards taunting the former dictator as he stood on the gallows.
Officials say they will take more precautions for the executions of Tikriti and Bander, including checking witnesses for cameras and mobile phones.
Tikriti and Bander were found guilty two months ago over the killings of 148 Shia men from the town of Dujail in the 1980s. Bander had presided over the court that ordered the men's deaths.
Tensions between Sunni and Shia Muslims remain high throughout Iraq this week in anticipation of the forthcoming executions.
Today, hundreds of Shia Muslims marched in the southern city of Basra to support the execution in a demonstration organised by the local office of Maliki's Dawa party.
Meanwhile, violence returned to the streets of Baghdad following a lull over the Eid holiday when two bombs exploded near a petrol station in the western Mansour district, killing at least 13 people and wounding 22.
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