The US military said on Sunday it was still unsure of the identity of Abu Omar al-Baghdadi, the man Baghdad says was the leader of Al-Qaeda in Iraq, but was trying to understand his role.
"We have nothing that contradicts the intelligence they have so far," US army Major General David Perkins said.
"We are not sure of the complete role this man played," Perkins told reporters.
"Part of what we are doing now is to try to determine who he was. It's not what he called himself, it is really more what did he plan."
Police announced on April 23 they had arrested Baghdadi in the capital, and released photographs a few days later showing a middle-aged man with dark skin and a close-cropped beard and moustache, wearing a black shirt.
Last week, they aired a video on the internet showing the interrogation of a man who explained how Al-Qaeda financed its activities in Iraq.
"I was born in 1969 and I'm from Diyala (province). I joined Al-Qaeda in 2005 and I formed the Islamic State of Iraq in 2006," the man said in the video.
"I named myself Abu Omar al-Baghdadi al-Husseini because the name Abu Omar represents the Sunnis and al-Baghdadi is the centre of Iraq and al-Husseini represents all of the people," he said.
There have been continuing doubts about whether the man in Iraqi custody is really Baghdadi as the Al-Qaeda frontman has been reported captured or killed several times in the past.
An Al-Qaeda front organisation, the Islamic State of Iraq, put out a statement on an Islamist website earlier this month denying that Baghdadi had been arrested.
US commanders have also at times expressed reservations about how much real influence Baghdadi exercises within Al-Qaeda.