Mar was among the first to announce that he would seek the nomination to replace former MP Lee Richardson.
He said while his family was initially supportive of his federal plans, they now feel it wouldn't be fair to his three kids.
Mar said he has informed his campaign team of his decision.
He also said he will continue his duties as alderman for Ward 8, as he had been doing during the campaign.
Others still in the race are former alderman and MLA Jon Lord, media consultant Joan Crockatt, businessman Jordan Katz and Stefan Spargo -- Richardson's former campaign manager.
Richardson stepped down as MP to serve as principal secretary to Premier Alison Redford.Suggest a correction