The Red Cross says Iraqi prisoners - Saddam Hussein included - must be released or charged ahead of a formal end of occupation on 30 June.
The US expects to hold thousands of Iraqis after 30 June
An ICRC official in Baghdad says the former Iraqi leader, designated a POW, cannot continue to be held by US forces after the conflict ends.
"His case is the same as all other prisoners of war," said Nadia Doumani.
However, the US says up to 5,000 prisoners deemed a threat to the coalition will remain in its custody.
It is not clear if this includes Saddam Hussein.
Iraqi Prime Minister Iyad Allawi said on Monday that all the current detainees - without exception - would be handed over to the Iraqi authorities.
"The handover will take place within the next two weeks," Mr Allawi told Arabic television station al-Jazeera.
"To be more precise, Saddam and the others will be handed over to the Iraqis, to the government."
Geneva Conventions say that if POWs are only being held because they are enemy combatants - not charged with any crime - they have to be released when the conflict ends.
An Iraqi tribunal is being set up to try the former Iraqi president and other prominent prisoners, although no formal charges have been issued to date.
A Senior British official said the tribunal would probably be able to start hearing cases later this year.
He said he did not know whether Saddam Hussein would be among the first to be put on trial.
Being released by 30 June does not mean detainees cannot be immediately rearrested by the newly-sovereign Iraqi authorities, the ICRC said.
"Saddam Hussein can be convicted for war crimes, for crimes against humanity... then he can be tried and prosecuted," said Ms Doumani, who speaks for the International Committee of the Red Cross in Baghdad.
"If he is not charged, then the law says that at the end of war, of occupation, he should be released," she added.
Saddam was seized eight months after his regime fell
Saddam Hussein has been held at an undisclosed location since his capture by US forces in December and is being interrogated by the CIA and FBI. He is expected to face charges of genocide and crimes against humanity.
The ICRC has paid two humanitarian visits to check the conditions under which he is being held.
US army spokesman Barry Johnson said on Sunday that up to 1,400 prisoners would be either released or transferred to the Iraqi authorities before 30 June.
However, between 4,000 and 5,000 prisoners would continue to be held, Lt-Col Johnson said.
He added that US command would also continue operating Abu Ghraib prison and Camp Bucca prison near Um Qasr.
Buses carrying 405 prisoners left Abu Ghraib on Monday morning, with another 112 to be set free on Tuesday, the US military said.
Relatives are holding a vigil for imprisoned Iraqis
Relatives are holding a vigil for detainees outside the notorious Saddam-era jail that has since become synonymous with prisoner abuses by US soldiers.
The released prisoners cursed US forces, with one middle-aged man saying: "They are oppressors. These are infidels and oppressors".
Iraqis are meant to run their own affairs after June 30 - with tens of thousands of foreign troops in the country as an invited multilateral security force.
"The situation on the ground determines the facts," Ms Doumani said, stressing that it remained to be seen whether the occupation effectively ends with the handover of sovereignty on 30 June.
The senior British official said that the status of security prisoners remained to be decided by the Interim Iraqi Government in consultation with the Coalition Authority.
But he indicated foreign troops of the proposed multi-national force would probably keep control of many of the prisoners under the broad authority of the IIG.