On his weekly radio show, Ford addressed reports that stemmed from videos that showed the mayor when he was strolling to the Taste of the Danforth street festival on Friday night.
Some of the people present at the street festival had suggested that Ford appeared drunk, as he mingled with members of the public and posed for some photographs.
But the mayor said Sunday that while he had been drinking beer, it did not go further than merely having a good time.
"Did I have a couple of beers? Absolutely, I had a couple of beers. But you know what, I had a good time, I think things are getting blown out of proportion," Ford told listeners on Newstalk 1010.
"I met a lot of people, took hundreds of pictures and if I offended anyone, you know what, I apologize."
Following the mayor’s appearance at the street festival, Coun. Jaye Robison reiterated her call for Ford to take a leave of absence to "address his personal problems and then come back to continue to act as the mayor of Toronto."
In the past year, Ford has on several occasions been accused of behaving strangely while at public events. But the mayor has consistently denied the allegations made about him.
In March, Sarah Thompson, a former mayoral candidate, accused Ford of groping her at an event and suggested that he could have been under the influence of drugs or have an undisclosed medical issue.
The mayor called her claims "absolutely, completely false."
That same month, the Toronto Star reported that Ford had been asked to leave a military fundraiser earlier in the year, as organizers were concerned he was impaired. The mayor called the report "an outright lie."
In May, reports emerged that someone had been shopping around a video of Ford that appeared to show the mayor smoking crack cocaine.
Ford denied using crack cocaine and also denied the video's existence.
The U.S. gossip website Gawker raised $201,204 in a bid to purchase the alleged video, but lost contact with the person who had offered to sell it and did not obtain it.