Abu Ghraib is located on the western outskirts of Baghdad and was used as a torture centre under ousted President Saddam Hussein.
It gained international notoriety when it was revealed that US forces had abused Iraqi detainees at the prison in 2003.
In February, SBS's Dateline revealed more photographs of alleged abuse of Abu Ghraib prisoners.
US military officials said the prison will be shut down once a new facility under construction near Baghdad airport is complete.
"We will transfer operations from Abu Ghraib to the new Camp Cropper once construction is completed there," said US detainee operations spokesman Lieutenant Colonel Kier-Kevin Curry in a statement.
Move within three months
"No precise dates have been set, but the plan is to accomplish this within the next two to three months," he said.
US military spokesman Lieutenant Colonel Barry Johnson said the Abu Ghraib facility would be handed over to the Iraqi authorities, "but we do not anticipate the Iraqi government to use it as a prison or a detention facility. However, it is up to them how to use it."
The Iraqi government currently operates its own prison within the grounds of Abu Ghraib.
The US military said it was responsible for 4,537 detainees at Abu Ghraib.
Lieutenant Curry said coalition forces and the Iraqi government were preparing for Iraqis to assume full control of detention operations.
He said a joint planning team meets regularly to develop the details of the transfer which involves training the Iraqis.
Lieutenant Curry said the four-step training involves a course on the basics of how to be a prison guard and how to work with coalition forces at the facilities.
"A specific timeline is difficult to project at this stage with so many
variables and the transition will be based on meeting standards, not on a timeline," he said.
Apart from those held at Abu Ghraib, the US military hold 8,607 detainees at Camp Bucca, in the south of the country, 127 at Camp Cropper, and 1,318 at Fort Suse, in the north of the country.
The International Committee of Red Cross (ICRC) said it hoped the transfer of detainees to the new facility would facilitate inspections by its officials.
"For us what is significant is the way in which the prisoners are treated," said ICRC spokesman Nada Doumani.
"If they are transferred we wish that it is to centres where the ICRC can visit them. The ICRC has not been able to visit Abu Ghraib for a year because of the security situation," he said.
Seven lower ranking US soldiers, described by Defence Secretary Donald Rumsfeld as "a few bad apples", faced courts martial over the abuse.
The ringleader, specialist Charles Graner and his girlfriend of the time, Private Lynndie England, became the public face of the abuse scandal.
Graner was jailed for 10 years, while England, who was pictured holding a naked prisoner at the end of a dog leash, was sentenced to three years jail and given a dishonorable discharge.
The prison commander at the time, Janis Karpinski, was the most senior officer to be reprimanded. She was demoted from brigadier general to colonel but faced no charges.
Latest violence
Meanwhile, at least five people have been killed and 12 others wounded in a car bombing near a Sunni mosque in east Baghdad.
Captain Mahir Hamad Mousa says the target was the Al-Israa Walmiraj mosque in the New Baghdad region of the capital.
The deaths bring to at least 16 the number of Iraqi civilians killed in bombings on Thursday.
Iraq executions
The Iraqi authorities have reportedly hanged 13 people accused of taking part in the insurgency.
"The competent authorities have today carried out the death sentences of 13 terrorists," a cabinet statement said.
The BBC reports that the authorities only released the name of one of those executed.
Shuqair Farid, a former policeman, allegedly confessed he had enlisted Iraqis to carry out attacks. Three convicted murderers were hanged last September.
If the reports are correct, they would be the first executions of militants since the US-led invasion.
The US-led coalition abolished the death penalty in Iraq after the overthrow of Saddam Hussein, but it was reinstated during the handover to Iraqi control in June 2004.
The Iraqi government wanted to give itself the option of executing the former president, who is currently on trial with seven others for the killing of 148 Shias from the village of Dujail in 1982.
New parliament
Meanwhile, Iraq's new parliament will hold its first meeting in just over a week on March 19, just over three months after it was elected, a spokesman for President Jalal Talabani told AFP on Thursday.
Members of the dominant Shiite United Iraqi Alliance (UIA) earlier the same day called on President Talabani to delay the opening of the new parliament by a week.
The request was accepted by all the other parties, said the President’s spokesman, Kamiran Karadari.
A decision on when to open parliament was earlier held up by a dispute between the Alliance and Mr Talabani, who is backed by the Sunnis and the Kurds.
The dispute centred on whether outgoing Shiite Prime Minister Ibrahim Jaafari -- the UIA candidate -- should be chosen to lead the next coalition government.
The announcement followed a closed-door meeting on Thursday of the three-man presidential council, headed by Mr Talabani, alongside Mr Jaafari and Iraq's deputy premiers, the outgoing speaker of parliament and the chief justice.