The US military and some analysts have even suggested that al-Baghdadi could be a fictional character created to give the group an Iraqi face.
The video released on Monday appeared to show the same person as the photographs released after al-Baghdadi's reported arrest.
"I was born in 1969 and I'm from Diyala. I joined al-Qaeda in 2005 and I formed the Islamic State of Iraq in 2006," the man in the video could be heard telling his interrogators.
"I named myself Abu Omar al-Baghdadi because the name Abu Omar represents the Sunnis and al-Baghdadi is the centre of Iraq"
Video purported to show Abu Omar al-Baghdadi, leader of al-Qaeda in Iraq
"I named myself Abu Omar al-Baghdadi 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.
The man then went to describe the funding of the group and claim responsibility for the bombing of a Shia shrine in Samarra in February 2006, which sparked sectarian violence that killed thousands of people across the country.
"The financing sources are external and internal. The external sources are from some associations based in Egypt, Saudi Arabia and Syria as well as some people who bring money to Iraq," he said.
"There are also internal sources derived from theft, or stolen from the salaries of employees."
Iraqi authorities have made a number of previous claims that al-Baghdadi has been either killed or captured that have proved to be incorrect.