Ford earlier acknowledged he smoked crack "probably a year ago" when he was in a "drunken stupor," but balked at growing pressure on him to resign.
"I was elected to do a job and that's exactly what I'm going to continue doing," Ford said. "On Oct. 27 of 2014, I want the people of this great city to decide whether they want Rob Ford to be their mayor."
The allegations that the mayor of Canada's largest city had been caught on video smoking crack surfaced in news reports in May. Ford initially insisted the video didn't exist, sidestepped questions about whether he had ever smoked crack and rebuffed growing calls on him to step down.
The mayor was forced to backtrack after police said last week they had obtained a copy of the video in the course of a drug investigation against a friend of Ford's.
"Yes, I have smoked crack cocaine," Ford told reporters earlier outside his office. "There have been times when I've been in a drunken stupor. That's why I want to see the tape. I want everyone in the city to see this tape. I don't even recall there being a tape or video. I want to see the state that I was in."
Police have said the video, which has not been released publicly, does not constitute enough evidence to charge the mayor with a crime.
Police spokesman Mark Pugush said Ford's acknowledgement of crack use will be passed on to investigators. Several Toronto city councilors called on Ford to step down and Canada's justice minister urged him to get help.
Ford, 44, earlier walked out of his office and asked reporters to ask him the question they first asked him in May. He then acknowledged he smoked crack but said: "Am I an addict? No. Have I tried it, probably in one of my drunken stupors a year ago."
Municipal law makes no provision for the mayor's forced removal from office unless he's convicted and jailed for a criminal offense.
City Councilor Denzil Minnan-Wong, a member of Ford's executive committee, said he would put forward a motion asking Ford to take a leave of absence.
"My first reaction was 'Wow'," Minnan-Wong said.
Councilor Jaye Robinson said the mayor needs to step aside and address his problems.
"We have become a laughing stock of North America, if not the world," Robinson said.
Canada's Justice Minister Peter MacKay said it was "a sad day for the city of Toronto."
"As a human being, I think the mayor of Toronto needs to get help," MacKay said.
Ford later told the Toronto Sun newspaper that he is not stepping down or taking a leave of absence.
"I feel like I got 1,000 pounds off my back," Ford told the paper, which is sympathetic to the mayor. "I felt like I had to say it. It is what it is. I feel two inches high right now but I needed to deal with it. I am not going to quit or take a leave."
The populist Ford has been dogged by allegations of bad behavior since becoming mayor three years ago, promising to end what he called wasteful spending at city hall. His campaign galvanized conservatives in Toronto's outlying suburbs, where initiatives like downtown bike lanes were considered excessive and elitist.
The crack episode is not the first time Ford has been forced to admit drug use. During the campaign, Ford acknowledged after repeated denials that he was busted for marijuana possession in Florida in 1999.
Ford apologized over the weekend for excessive drinking. He said he shouldn't have been drunk in public when he appeared at a street festival in August, calling it "pure stupidity."
He also said he got "a little out of control" after St. Patrick's Day in 2012, when city hall security guards said they witnessed a "very intoxicated' Ford having trouble walking and swearing at aides.
Ford said he was "hammered" at that street festival this summer.
The mayor has also been accused of make an obscene gesture from his car and texting while driving. In 2011, Ford angered the city's gay community by declining to attend Toronto's gay pride parade, breaking with tradition that three previous mayors had kept up.
Earlier this year, the mayor was fired from his cherished side-job as a volunteer high school football coach after he made disparaging remarks to a TV network about parents and their kids.
On Tuesday, Ford's brother, Doug, criticized Police Chief Bill Blair for saying he was "disappointed" in the mayor after police recovered the tape last week. Doug Ford called the chief's comments "inappropriate" and "biased" and said Blair should step aside.
"We have the most political police chief we have ever seen," said Doug Ford, an influential city councilor. "The police chief believes he's the judge, the jury and the executioner."
Blair says he responded honestly when asked about his feelings after watching the video.
The allegations about Ford smoking crack surfaced when two reporters with the Toronto Star and one from the U.S. website Gawker said they saw the video but they did not obtain a copy. Ford vilified the Toronto Star, accusing the paper of trying to take him down.
The mayor has called on the police to release the tape, but police said they are prohibited from doing so because it is evidence before the courts.
Police said the video will come out when Ford's associate and occasional driver, Alexander Lisi, goes to trial on drug and extortion charges. Lisi is accused of threatening two alleged gang members who had been trying to sell the video to the media.
Police have said they want to talk to the mayor, but his lawyer so far has declined.