Al-Qaida in Iraq posted a second internet statement boasting that its fighters carried out the bold attempt on Saturday to force their way into the prison.
The statement said two fighters were injured and 10 more were killed in battle, including seven bombers.
The statement was impossible to independently verify, and it conflicted with the US account of the assault.
US military officials said on Monday that only one bomber was used in Saturday's attack, along with gunfire, mortar rounds and rocket-propelled grenades. At least one fighter was killed.
More than 40 US servicemen and 13 prisoners were injured in the attacks.
Abu Ghraib was at the centre of a prison abuse scandal last year after photographs became public that showed US soldiers humiliating and abusing Iraqi inmates, including sexually.
The United States is holding 10,500 prisoners in Iraq, with nearly 3500 of them at Abu Ghraib.
Abu Ghraib prison has now been
targeted twice in 48 hours
Meanwhile, Aljazeera learned that a bomber detonated his explosive-laden car at the main gate of the prison on Monday.
Sources from Abu Ghraib area told Aljazeera that five Iraqis were injured in addition to US casualties.
Soldiers stationed at the detention facility responded and the fight lasted about 40 minutes, the US military said.
Aljazeera also learned that fierce clashes erupted between US forces and armed fighters in al-Ghazaliya neighbourhood, west of Baghdad, on Monday.
US military vehicles poured into the area, closing off all connecting roads, while military helicopters were seen flying overhead.
Saturday's attack on Abu Ghraib
prison wounded 44 US soldiers
The US military disclosed on Monday that armed men shot dead a US soldier and wounded another in the northern Iraqi town of Tal Afar on Saturday.
Tal Afar, west of Mosul on the road to the Syrian border, has seen frequent attacks.
Since the invasion in March 2003, at least 1165 US military personnel have been killed in action in Iraq.
Earlier, speaking from the UAE, Iraqi political analyst Dhafir al-Ani told Aljazeera that Abu Ghraib prison was a legitimate target because it was under complete US jurisdiction.
"It is completely out of the control of the Iraqi government and police," al-Ani said.
"In addition, a number of Iraqi national resistance figures are detained in that prison. Many attacks against the prison were attempts to release them."