Last week Terry Jones, a controversial Christian preacher who presides over a small church in Florida, drew international condemnation after announcing a plan to burn 200 copies of the Koran.
"With respect to books like the Bible and the Koran, whatever, just get over it," Mr Stewart said in the footage. "The video was a joke video, of course," he added.
"People do this stuff all the time and if people get really upset about this then they're taking it far too seriously."
Mr Stewart, a member of an atheist group in Brisbane, has begun a period of leave following a meeting with his employers today. He insists he wasn't smoking drugs in the video but had sprinkled grass cuttings into the rolled up pages.
"The university is obviously extremely, extremely unhappy and disappointed that this sort of incident should occur," Queensland University of Technology vice-chancellor Peter Coaldrake said.
Islamic groups urged Muslims not to react to the provocation