Craig told CNN he is no longer pursuing the job because "FEMA doesn't need the sidetrack right now" -- referencing an NBC News report
that investigators had probed the work and travel records he submitted while working as an official in the George W. Bush administration.
The revelation of that investigation by the Department of Homeland Security inspector general, completed in 2011 but first disclosed by NBC on Wednesday, would prevent his nomination from advancing in the Senate, Craig said.
Craig was nominated by President Donald Trump in July to be the deputy administrator of FEMA, which is currently busy responding to devastation from hurricanes Harvey and Irma.
But acting Homeland Security Secretary Elaine Duke said in a statement that Craig "would have been a major asset" in that response.
On Wednesday, NBC reported that the inspector general report had "found he had falsified government travel and timekeeping records when he served in the Bush administration in 2005."
But, NBC reported, neither the inspector general nor the FBI charged Craig with a crime.
The DHS inspector general's office acknowledged that the report exists. But spokesman Arlen Morales told CNN the report is not publicly available "due to protections that the Privacy Act affords the individuals named in the report."
Craig said he first saw the 2011 report on Monday.
"In my opinion the (Office of Inspector General) did nearly a five-year investigation and need to have something to show for it, so they only look at things which supported their conclusion," he told CNN.
White House press secretary Sarah Sanders would not say whether Trump was aware of the investigation when he nominated Craig. To discuss that, she said Wednesday, would be "to go down rabbit holes on personnel."