Michael Brown, in an interview with CNN, accused Chertoff of lacking disaster management knowledge.
Brown resigned from the Federal Emergency Management Agency in September amid intense criticism of his performance after Katrina, the Aug. 29 storm that left more than 1,300 dead in Louisiana, Mississippi, Alabama and Florida.
Brown blamed the poor federal response on the dysfunctional structure of the Department of Homeland Security, which became FEMA's parent agency when Homeland Security was established in 2003.
"It appears to me that, you know, when Chertoff does things like tells me that I've got to go to Baton Rouge and plop my butt down on a seat in Baton Rouge and run a disaster from there, I think that shows naiveté about how disasters are run," Brown told CNN.
Asked whether Chertoff should be dismissed, Brown said, "Well, I think so."