"We will allow your withdrawal to complete without anyone targeting you with any explosive or anything else," a speaker identified as Abu Omar al-Baghdadi, the leader of the Mujahedin Shura Council, said on an audiotape, CNN reported.
He said U.S. forces must also leave heavy weaponry behind and turn over their military bases "to the mujahedin of the Islamic state."
"We say to Bush not to waste this historic opportunity that will guarantee you a safe withdrawal," Baghdadi said on the tape. The authenticity of the recording could not be verified, CNN said.
He gave Washington two weeks to respond to the offer.
The U.S. military had no immediate reponse.
The Mujahedin Shura Council is an umbrella group formed in late 2005 that includes several terrorist and insurgent groups, including al-Qaida.