Hudayf Azzam, 35, who claims close contacts with the fighters, said on Sunday: "The Iraqi resistance's high command asked Zarqawi to give up his political role and replaced him with an Iraqi, because of several mistakes he made.
"Zarqawi's role has been limited to military action. Zarqawi bowed to the orders two weeks ago and was replaced by Iraqi national Abdullah bin Rashed al-Baghdadi."
Azzam's late father, Abdallah Azzam, was known as the "prince of mujahedeens" and advised bin Laden, the head of al-Qaeda.
Azzam said he regularly receives "credible information on the resistance in Iraq. He said al-Zarqawi had "made many political mistakes", including "the creation of an independent organisation, al-Qaeda in Iraq".
"Zarqawi also took the liberty of speaking in the name of the Iraqi people and resistance, a role which belongs only to the Iraqis," Azzam said.
As a result "the resistance command inside and outside Iraq, including imams, criticised him and after long discussions demanded that he be confined to military action".
"Zarqawi pledged not to carry out any more attacks against Iraq's neighbours after having been criticised for these operations which are considered a violation of sharia [Islamic law]," Azzam said.