Kofi Annan, Ban's predecessor, opposed the death penalty as a matter of policy, along with many other UN officials and all members of the European Union.
Following the barrage of criticism, Ban urged Iraq on Wednesday to stay executions after Louise Arbour, the UN high commissioner for human rights, appealed to Iraq not to put to death two Iraqi officials who served under Saddam.
Saddam's hanging angered other Sunni Arabs after video images showed Shia officials taunting him while he was on the gallows.
Saddam's execution had been rushed through four days after he lost an appeal against his death sentence.
Barzan al-Tikriti, Saddam's half-brother and former intelligence chief, and Awad al-Bander, a former chief judge, were also found guilty along with Saddam of crimes against humanity in the killings of 148 Shia men from Dujail in 1982.
The Iraqi government has not set a date for execution of the two men, but in Iraq there is increasing speculation that they will be executed within days.