Allawi promised an open proceeding when Saddam faces war crimes charges, including genocide. Eleven others "high-value detainees" also are expected to face justice, he told reporters during his first news conference since the U.S.-led coalition handed over sovereignty to his government on Monday.
"I know I speak for my fellow countrymen when I say I look forward to the day former regime leaders face justice," he said.
However, the trials for Saddam and 11 others will not occur for months and he urged the Iraqi people to be patient.
But he insisted that Saddam must receive a "just trial, a fair trial."
"We would like to show the world that the new Iraq government means business and wants to do business and wants to stabilize Iraq and put it on the road toward democracy and peace," Allawi said. "We want to put this bad history behind us and move toward a spirit of national unity and reconciliation in the future."
Iraqi authorities announced arrest warrants for Saddam and the 11 others, including former Deputy Prime Minister Tariq Aziz.
Allawi did not identify any other defendants due to be handed over.
However, a Saudi Web site, Elaph.com, quoted Iraqi sources as saying the list includes Ali Hassan al-Majid, also known as "Chemical Ali"; former Vice President Taha Yassin Ramadan; Aziz; and two of Saddam's half-brothers.
Allawi said the Iraqi Cabinet still discussing whether to reinstate the death penalty.
Justice Minister Malik Dohan al-Hassan said Saddam could have foreign lawyer — if Iraqi lawyers' association agrees.
The Jordanian lawyer claiming to represent Saddam has argued that the ousted leader should be released because handing him over to Iraq's new government would violate international law.
Ziad al-Khasawneh, one of 20 Jordanian and foreign lawyers appointed by Saddam's wife, Sajidah, said the United States has no legal basis to keep prisoners, including the ousted ruler, now that it has transferred authority to an interim Iraqi government.
Jacques Verges, an 80-year-old French lawyer, has also. He has promised to put the spotlight on the United States for its years of support of Saddam, and to call such witnesses as Secretary of Defense Donald Rumsfeld.
Despite the change in legal custody, the former Iraqi leader will remain in a U.S.-run jail because the Iraqi government lacks a suitable prison.
That creates a delicate diplomatic situation, reports CBS News Anchor Dan Rather. The U.S. wants to maintain physical custody of Saddam but want him to be seen in public in the hands of the new Iraqi government.
National Security Adviser Mouwafak al-Rubaie told CBS News on Monday that in the transfer of custody on Wednesday, two U.S. soldiers will take the handcuffed former dictator from his cell and give him over to four Iraqi policemen. Saddam will then stand uncuffed in front of a judge.
"The judge is going to give him his rights and his defense and he's going to read him the rights and he's going to issue an arrest warrant against Saddam Hussein," says al-Rubaie.
Saddam will then be chained again and marched back to a cell.
Iraqis will see images of Saddam under their country's system of justice, and in handcuffs in the custody of his own countrymen, facing a process he denied to countless Iraqis, says al-Rubaie.
Saddam, who was captured by U.S. troops in Dec. 13, is being kept at an undisclosed location in or near Baghdad and has been interrogated by the CIA and FBI.
The International Committee of the Red Cross has indicated that under international law, Saddam must be charged or released after the formal end of the occupation since he was detained as a prisoner of war.
The tribunal that will try Saddam has a budget of $75 million. It will rely on a mix of Iraqi criminal law, international regulations such as the Geneva Convention and experiences of bodies such as the Rwanda war crimes tribunal.
Judges have refused to work for the tribunal after five potential candidates were killed since Saddam was toppled from power last year.
Allawi said that more than 1 million Iraqis are missing as a result of events that occurred during the former regime. That figure is more than twice the 400,000 that British Prime Minister Tony Blair has said ended up in mass graves.
It is unclear what crimes Saddam will be charged with committing.
The nonprofit group Indict, which has pressed for years for Saddam to be prosecuted for war crimes charges, contends he is guilty of aggression in wars against Iran and Kuwait, genocide for campaigns against the March Arabs and curds, crimes against humanity for using chemical weapons and brutally suppressing the 1991 Shiite revolt, and torture.
The Iraqi tribunal is empowered to prosecute war crimes, genocide, crimes against humanity and violations of specified Iraqi law.
The U.S. Justice Department has been gathering evidence for a war crimes case against Saddam, while other international groups have been sifting through the mass graves where U.S. officials say victims of Saddam's regime were buried.