Olsson said on Swedish Radio that the academy had been in "full agreement" to postpone the 2018 award since "there really was no other alternative". The academy said Friday the 2018 prize will be given in 2019.
Responding to the announcement Friday, close observers of the Swedish Academy's handling of the scandal said that the committee essentially had no other choice than to postpone this year's prize. He wrote that it was acting "out of respect for previous and future literature laureates, the Nobel Foundation and the general public".
Three members of the Swedish Academy's board resigned because of dissatisfaction over the way an investigation into the allegations was conducted.
This happens to be the first time that the award would be cancelled for political reasons.
No worthy victor was present in 1935.
The dramatic move came after allegations to Swedish media outlets that photographer Jean-Claude Arnault, the 71-year-old husband of poet and Academy member Katarina Frostenson, had sexually assaulted or harassed 18 women - and years ago groped Crown Princess Victoria of Sweden.
Mr Arnault has denied all allegations regarding both sexual misconduct and leaking the names of laureates, his lawyer told Reuters on Thursday.
Frostenson was also alleged to have violated the academy's conflict-of-interest rules by failing to disclose she was co-owner of a performance venue run by her husband, which formerly received funding from the academy.
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A reform of the organization will soon allow members to leave voluntarily, so that they can be replaced by successors. It was not until 27 years later - in 2016 - that the Academy finally condemned the fatwa against Rushdie.
Statutes require a quorum of 12 to vote in any new members.
The academy said that the organization's "operative practices need to be evolved". Two prizes will be conferred in 2019.
The #MeToo campaign, which showed the prevalence of sexual assault globally, may have played a part in the academy's decision. It would have been hard for potential winners to accept the prize with the academy in such turmoil.
The Nobel Foundation reacted promptly, saying it presumes the academy "will now put all its efforts into the task of restoring its credibility as a prize-awarding institution".
The awards are decided by different bodies.
The problems at the Swedish Academy began last fall.
The academy was founded in 1786 as the arbiter of Swedish language and letters, and was designated by Nobel, in his will, to award the literature prize in his name. Besides the six years during the world wars, there has only been one year when the prize was not awarded and that is because no victor was found in 1935.