"I'm the first one to admit I am not perfect, I have made mistakes," Ford told his weekly radio show.
"Unfortunately, I cannot change the past, I can just move forward and learn from the past," he said, his voice at times choked with emotion.
"I also know that to move forward I have to make changes in my life, which I will assure you I can do," he said. "I want to keep working for the people of this city."
Ford apologized to his family, members of city council and Toronto taxpayers. He said he was referring to being inebriated in public and texting while driving.
"A lot of stupid things, it's all self-inflicted," he said.
Ford didn't talk about the contents of the video that police say seems to be the one that two media outlets say allegedly appears to show him smoking crack cocaine.
"Obviously when the video is released, I'm going to explain to the best of my ability what's in the video," said Ford, who called on police Chief Bill Blair to release the video so everyone can see it.
"Whatever this video shows, folks, Toronto residents deserve to see and people need to judge for themselves what they see on this video," Ford said on the show, broadcast on Toronto radio station NewsTalk 1010.
"That is the right thing to do and chief, I'm asking you to release this video now."
But when the scandal first broke in May, Ford insisted there was no video at all.
"I cannot comment on a video that I have never seen or does not exist," he said then.
Ford said later Sunday in a separate interview that he does not have a drug addiction problem.
"I’m going to reiterate what I said before. I am not a crack addict. I’m not an addict of any type of drug -- even alcohol. I’m not an alcoholic," he told Toronto radio station AM640 in an interview.
Blair said Thursday that the video will be evidence in the case against Alexander Lisi — a friend and sometimes driver for the mayor. Police allege Lisi tried to get his hands on the video and charged him with extortion.
Lisi appeared in court on Friday and was granted bail.
Toronto police said Sunday that it is up to the courts to decide whether evidence is released to the general public.
After reports of the alleged video first surfaced in the Toronto Star and the U.S. website Gawker, the mayor said he does not use crack cocaine.
He steadfastly refused to talk about the issue for months, but Blair's stunning announcement last Thursday that police had what appeared to be the video triggered a torrent of calls for Ford to either resign or address the issue.
Ford met privately Saturday with deputy mayor Norm Kelly, who relayed concerns from city councillors about the fallout from the police revelations.
Kelly appealed on Sunday for everyone, including Ford's critics on city council, to give the mayor a second chance.
"I would urge my colleagues to do that, to show that this is more than just rhetoric... that in fact he has learned his lesson," Kelly told The Canadian Press in a phone interview after the radio show.
Kelly said Ford addressed a number of the concerns councillors asked him to pass on to the mayor on Saturday, including acknowledging the impact of some of his actions and promising to get a full-time chauffeur to drive him.
The video saga earned Ford international headlines, with countless foreign media devoting space on their websites to the story.
On top of the video story, there have been repeated accounts of Ford appearing intoxicated in public. On Sunday he acknowledged having too much to drink during a Toronto street festival last summer.
"I shouldn't have got hammered on the Danforth," Ford said of the Greek street festival in the city's east end.
At the time of the festival Ford downplayed his behaviour at the street festival, saying in August that he didn't do anything offensive and that videos of him appearing intoxicated at the event were blown out of proportion.
Ford also admitted he drank too much on St Patrick's Day last year.
The Toronto Star reported Friday that security guards indicated Ford was very intoxicated and struggling to walk and swore at one of his staff members.
The Star said the account was in an incident report sent by one of the guards to a supervisor and was released through freedom of information.
And after hearing the mayor's apology for his bad behaviour and his promises to clean up his act, some Toronto residents remained unforgiving.
Mike Dukelow said Ford should step aside.
"I think basically he's making a mistake and he should step down until it's resolved or charged," Dukelow said, adding the scandal is hurting the city's reputation.
"I don't think any big town or small town needs that type of notoriety."
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