At least 40 fighters fired rocket-propelled grenades and set off two car bombs on Saturday at the infamous prison as darkness fell, 1st Lieutenant Adam Rondeau said.
Soldiers stationed at the detention facility responded, and the fight lasted about 40 minutes, the US military said.
"This was obviously a very well-organised attack and a very big attack," Rondeau said. On Sunday, US military officials raised the casualty toll from 20 to 44 US service members. Some of the injuries were serious.
Late on Sunday, a US soldier was killed in a bomb blast outside the Iraqi refinery town of Baiji, 200km north of Baghdad, the US military said.
"One Task Force Liberty soldier was killed when an improvised explosive device detonated around 6.45pm on 3 April. The attack occurred near Baiji," the statement read.
Death lurks at every corner for
US troops on foot patrol in Iraq
The death brings to 1529 the number of US military personnel who have died in Iraq since the US-led invasion two years ago, according to a tally based on Pentagon figures.
Officials have said that attacks have been declining in Iraq overall, but they have noted that fighters are focusing on bigger and better organised operations.
It was not immediately known if any of the fighters were arrested or suffered casualties. Plumes of smoke were seen rising from the area.
Abu Ghraib was at the centre of a prisoner-abuse scandal that broke out in 2004, when pictures showing soldiers piling naked inmates in a pyramid and humiliating them sexually became public.
The resulting scandal tarnished the US military's image worldwide and sparked investigations of detainee abuses. The US is holding about 10,500 prisoners in Iraq.