Mr Ford is under pressure after Canadian police revealed they had recovered a video appearing to show him smoking from a crack cocaine pipe.
On Monday, he said in an interview he was "not a drug addict". He has called for police to release the video.
He said he would not resign and vowed to run for re-election next year.
"If I had a problem, I'd be the first one to say I'm not fit to run the city," he said during a local radio interview on Monday.
The mayor added that while he enjoys "a few cocktails", he was "not an alcoholic".
"Have I drank a little too much at times? You're absolutely right," he said. "Am I going to curb that? Absolutely I'm going to curb that."