Richard Falk, a retired professor from Princeton University, wrote on his blog that there had been an "apparent cover up" by American authorities on the matter, and added that most media were "unwilling to acknowledge the well-evidenced doubts about the official version of the events" on 9/11, despite it containing "gaps and contradictions".
He further described David Ray Griffin, a conspiracy theorist highly regarded in the so-called "9/11 truth" movement, as a "scholar of high integrity" whose book on the subject was "authoritative".
Ban described Falk's comments as "preposterous" and "an affront to the memory of the more than 3,000 people who died in the attack," The Telegraph reports.
However, Ban said that it is not his duty to decide whether Professor Falk, the UN special investigator into human rights abuses in the Palestinian territories, should be fired by the organisation.
Ban's chief of staff, Vijay Nambiar, said that the human rights council, a 47-nation body based in Geneva, Switzerland, that was created by the UN in 2006, should take the decision whether or not he should be sacked. UN Watch, a pressure group that monitors the organisation, has demanded for Falk's removal, with its Chief Executive Hilel Neuer calling him "a serial offender with zero credibility".
The row came as the new Republican-led US Congress opened an inquiry into "urgent problems" with America's contribution to the UN, including its membership of the human rights council.