"Interrogations and investigations are still under way to get more information," he said.
Al-Moussawi had previously said that al-Baghdadi had been captured in a raid in Abu Ghraib on the outskirts of Baghdad, a report later verified by a senior adviser to Nuri al-Maliki, the Iraqi prime minister.
"One of the terrorists who was arrested with him confessed that the one in our hands is al-Baghdadi," al-Moussawi said on Iraqiya state television on Friday.
Al-Baghdadi, also known as Abu Abdullah Rashid al-Baghdadi, has been identified in statements posted on websites as the self-styled head of the Islamic State of Iraq, proclaimed last year after the death of Abu Musab al-Zarqawi, the leader of al-Qaeda in Iraq.
The Islamic State of Iraq, said to be linked to al-Qaeda and armed Sunni groups, has claimed responsibility for a string of major attacks.
US and Iraqi forces have increasingly focused on al-Baghdadi's group in their attempts to end sectarian vioence in Iraq.
Al-Baghdadi is also said to have headed the Mujahidin Shura Council, an alliance of al-Qaeda and other hardline groups. Very little is known about al-Baghdadi and his capture would be hard for officials to verify.