He told reporters he was "very keen" Chairman Paul Volcker, a former head of the U.S. Federal Reserve and his two colleagues heading up the inquiry, will "really get to work and give us a report as soon as possible."
Annan said former program head Benon Sevan, "Should and will be available for the investigation, and we are discussing how to make sure that he will be available."
"He has indicated he will cooperate as I expect all other staff members to cooperate."
Sevan has denied numerous published allegations.
"It is unfortunate that there have been so many allegations," Annan said, "And some of it is being handled as if they were facts, and this is why we need to have this investigation done."