"Let’s just get on with it," Stintz said, when speaking with reporters at Toronto City Hall.
"The mayor has already indicated that he is not going to take a leave of absence, that he is not going to resign, so we need to take the mayor at his word and we need to continue on with the business of the city."
Over the weekend, Ford restated his intention to stay in his job, despite increasing pressure from critics and councillors to take a leave of absence.
Ford also apologized for "mistakes," some of which were left unspecified, but which the mayor said included a pair of episodes in which his alcohol-related behaviour led to problems.
"For example, the Danforth, that was pure stupidity. I shouldn’t have got hammered down at the Danforth. If you’re going to have a couple of drinks, you stay at home and that’s it, you don’t make a public spectacle of yourself," Ford told the listeners of his Sunday radio show on Newstalk 1010.
During the same broadcast, Ford called on Toronto police Chief Bill Blair to release a video file, which investigators obtained from an electronic device that was seized during a series of police raids earlier this year.
While Blair did not say what was on the video, he said it featured the mayor and its content was "consistent" with press reports that had described it.
Earlier this year, the Toronto Star and the U.S. gossip website Gawker reported that someone had been shopping a video of the mayor in which he allegedly smoked crack cocaine. The mayor denied both the video’s existence and using crack cocaine.
The fact that Ford’s weekend apology didn’t address the allegations didn’t sit well with some councillors.
"I think it was minimalist. I don’t think it was adequate, it didn’t address what most people were very concerned about, which were the drug allegations," Coun. Gloria Lindsay Luby told reporters Monday, when asked about the mayor’s radio apology.
Luby said she wants Ford to take a leave of absence, though she expects "he certainly will try" to stay on until the next election.
Ford, 44, is only in the third year of his four-year term as mayor. He is intending to seek a second term.
Stintz, who has served as the TTC chair during Ford’s tenure, is the only current member of council to put her name forward as a mayoral contender so far. Former councillor David Soknacki is also set to run for mayor next year.
Ford has said he believes the coming mayoral election campaign in 2014 will be "a bloodbath."
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