Council finance convenor Willie Young claimed pulling out could have cost the authority Â£100m in cancellation fees.
The council later said there would be no financial penalty.
SNP Aberdeen Central MSP Kevin Stewart said he had written to council chief executive Angela Scott calling for an investigation.
Mr Young said earlier this week of his original comments: "It's unfortunate when I said that I wasn't in possession of all of the facts. As far as I'm concerned, having spoken to our officers, that was exactly the position that I was advised."
Planning permission for the development was granted in October.
Developer Muse has said it would be a "world-class development", but protesters fear it will block the view of the historic Marischal College and Provost Skene House.
An MSP has called for an investigation into whether the public has been "misled" about aspects of the Marischal Square plans in Aberdeen.