Rob Ford released a statement denying Sarah Thomson's allegations, which were made via Facebook and in a series of interviews with local media outlets.
Ford said he was "shocked, dismayed and surprised" to learn of the claims from Thomson, who ran against him for the city's top job in 2010.
He described the allegations as "completely false" while also criticizing her for launching her allegations on International Women's Day.
"What is more surprising is that a woman who has aspired to be a civic leader would cry wolf on a day where we should be celebrating women across the globe," Ford said in the statement.
"It is a day when we can envision the changes we want to make in our communities to ensure that all people are equal and that violence and discrimination against women comes to an end."
Thomson said the contentious encounter took place Thursday night at a Canadian Jewish Political Affairs Committee party when she asked why he had missed an event last week.
"He said, 'I was in Florida. You should have come with me, you know, my wife wasn't there.' And I'm looking at him going, 'What?'" Thomson told radio station NewsTalk 1010 on Friday.
"Then he said, 'Yeah, we could have had some fun.' And I kind of thought, 'OK, this is not him. This is weird.' And then I just turned and got my picture taken and he grabbed my ass and I'm thinking, 'What the heck is going on with him?'"
Thomson, publisher of the Women's Post and a transit activist, said she asked Ford what was wrong with him and he laughed it off.
"I walked away and I wanted to punch him in the face. You know, it's just one of those things where you just kind of go, how dare you?"
Ford seemed out of it, Thomson said, suggesting he might have a substance abuse problem, though she said he didn't appear inebriated.
Ford did not address Thomson's allegations of substance abuse in his statement, but his chief of staff Mark Towhey denied his boss was intoxicated.
"He didn't drink anything that night except three or four glasses of water and a bottle of water that I brought him," Towhey told the same radio station.
Thomson later backed down from that allegation, saying outside city hall Friday morning that she shouldn't have said that. She did, however, reiterate that he was behaving strangely, saying he is normally professional and respectful toward women.
"I don't know what it was," she said. "He needs to get help."
Thomson posted on Facebook the picture in which she says the unwanted touching took place and the mayor is seen with his eyes closed, mouth open and a large stain on his shirt in the middle of his chest.
She later conceded, however, that the picture was taken later in the evening and that she had deliberately returned to the function in order to get a shot of the mayor.
"We went back to say . . . 'let's do this, we have to do this. We should catch him. We have to get him out, he should not be doing this to women'," she said in an evening interview with NewsTalk 1010.
Towhey said Ford's team is talking to lawyers to determine "an appropriate course."
"I know the three staff never heard any of the comments that she's alleged," he told the radio station. "I know that the mayor was in Florida with his wife and children last week."
She appeared happy when she walked away after taking a photograph with Ford, Towhey added.
Ontario Premier Kathleen Wynne had attended the same function, but said she left the party before Ford arrived.
_ With files from Hailey Chan.