Ford called the allegations "ridiculous."
The video has not been released publicly, and there is no way to verify whether it is authentic. Reports by gossip website Gawker and the Toronto Star said it was taken by a man who claimed he had sold crack to Ford. The Associated Press hasn't seen the video.
The conservative mayor of Canada's largest city refused to take questions yesterday. In brief comments outside his office, he said it was "another story with respect to the Toronto Star going after me. And that's all I've got to say for now."
The Star reported that two reporters watched a video that appears to show Ford, sitting in a chair, inhaling from what appears to be a glass crack pipe. The Star said it did not obtain the video or pay to watch it.
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The Star also reported that Ford made an anti-gay slur against the leader of the federal Liberal Party of Canada, Justin Trudeau.
Ford later appeared yesterday at a previously scheduled ceremony marking International Day Against Homophobia.
During his campaign for mayor, Ford held a news conference to discuss a 1999 arrest for marijuana possession in Florida. He ultimately pleaded guilty to driving under the influence and failing to give a breath sample to police.
While in office, he has been accused of flouting conflict of interest rules and making obscene gestures at residents from his car.
Toronto deputy mayor Doug Holyday questioned the authenticity of the video, saying "video can be altered" and "drug dealers can't be trusted."
Holyday said he has not spoken to Ford or his staff since the allegations surfaced, but noted he still believes in the mayor "at this point.