New UN Secretary General Ban Ki-moon has urged
His appeal comes amid growing international criticism of the handling of Saddam Hussein's hanging, at which he was taunted and filmed.
Mr Ban was criticized this week for failing to state the UN's policy of opposing the death penalty.
Saddam Hussein's intelligence chief and chief judge are also due to be hanged.
Barzan Ibrahim al-Tikriti and Awad al-Bandar were convicted along with Saddam Hussein for their part in the killing of 148 Shia Muslims in the Iraqi
Saddam Hussein was hanged on 30 December.
Campaign
In a letter to the Iraqi representative at the UN, Mr Ban urged restraint in carrying out death sentences imposed by the Iraqi High Tribunal.
The BBC's Keith Adams says Mr Ban's comments on Saddam Hussein's hanging caused a stir this week - his first in the job.
He said capital punishment "was for each and every member state to decide" - words that seemed at odds with the UN's policy of opposing the death penalty.
Our correspondent says Mr Ban now seems to be asserting the established UN stance.
The UN said Mr Ban's letter "also refers to the secretary general's view that all members of the international community should pay due regard to all aspects of international humanitarian and human rights laws".
Iraqi Prime Minister Nouri Maliki has reacted angrily to the international outcry over the execution.
He said his government could review relations with any country that criticized the action.
Mr Maliki said the hanging was a "domestic affair" for the benefit of
International protest has continued, however. On Saturday
Former Italian Prime Minister Silvio Berlusconi called the execution a "political and historic error".
The
He said the manner of Saddam Hussein's death would do nothing to ease the tension between Sunnis and Shias.
Several Sunni Arab countries have criticized the hanging as sectarian.
Egyptian President Hosni Mubarak said it had turned the former leader into a martyr.
Photo caption
Ban ki-moon