Iraqi Governing Council member Ahmad Chalabi said on Wednesday that the captured former Iraqi president should be tried by Iraqis and face execution.
His calls were backed up earlier in the day by US president George Bush.
Bush suggested Hussein should receive "the ultimate penalty".
He told ABC television: "He is a torturer, a murderer, and they had rape rooms, and this is a disgusting tyrant who deserves justice, the ultimate justice."
But others, including the Iranian president, the UN secretary-general, the European Commission and several European countries have voiced opposition to capital punishment.
Iran's President Muhammad Khatami said, "I don't like the death penalty, although, if there is one case where there should be an execution, the fairest case would be for Saddam. But I would never wish for that."
Bush wants Saddam penalised
Khatami's comments on Wednesday are believed to be the first time he has voiced his unease with the death penalty, which is applied in Iran for certain serious crimes.
The president's comments come despite the fact that hundred of thousands of Iranians died as a result of the 1980 Iraqi invasion of Iran and the subsequent eight-year war.
UN Secretary General Kofi Annan said: "This should be done through open trials in properly established courts of law which will respect basic international norms and standards, including respect for international humanitarian law."
Position of principle
A spokesman for the European Commission, the executive arm of the 15-national European Union, said the EU's rejection of capital punishment is very clear.
"I don't like the death penalty, although, if there is one case where there should be an execution, the fairest case would be for Saddam"
President of Iran
"It's a position of principle, whatever the circumstances, the
gravity of the crimes committed," said Diego Ojeda.
A French foreign ministry spokesman said,"If it concerns the death penalty, you know our position, which is also that of the European Union," said a French foreign ministry spokesman.
The Dutch Foreign Minister Ben Bot said the Netherlands would
support any tribunal set up to judge the old dictator, but not if it contemplated execution as a possibility.
Italian Defense Minister Antonio Martino said he personally
opposes the death penalty and added, "I am not alone. The government and the great majority of the Italian people are against the death penalty."
Spanish Justice Minister Jose Maria Michavila said Spain wanted to see a "just sentence" passed against Saddam, but anything short of the death penalty.