Ford read a statement at City Hall, hours after admitting he had smoked crack, saying he was "elected to do a job and that's exactly what I am going to continue doing."
"In 2010 I made a commitment to Toronto voters," he said. "I have delivered on that commitment and I will continue to deliver on that commitment of saving taxpayers money."
He said he would leave it to voters to decide in October 2014 "whether they want Rob Ford to be their mayor."
In the afternoon news conference, Ford said he "will be forever sorry" for having embarrassed Toronto.
"There is only one person to blame for this and that is myself," he said. "I know that admitting my mistake was the right thing to do and it's like 1,000 pounds have been lifted of my shoulders."
He assured the public he has "nothing left to hide" and said "these mistakes will never, ever, ever happen again."
"There is important work that we must advance and important decisions that must be made," he said. "For the sake of the taxpayers we must get back to work immediately."
When reports first surfaced in May that a cellphone video showed Ford smoking crack, he told reporters the allegation was "ridiculous," and an attorney for Ford told the Toronto Star its report on the allegation contained "false and defamatory" details.
Toronto police last week said they have video of Ford smoking from what appeared to be a crack pipe.
In his earlier remarks to reporters at City Hall Tuesday, Ford prompted one to repeat the question, the Star reported.
"You asked me a question back in May. You can repeat the question," Ford said.
"Yes, I have smoked crack cocaine," he said.
Asked why he waited until now to admit he smoke crack, Ford said: "I wasn't lying. You didn't ask the correct questions."
Asked when he smoked crack, the mayor said: "I don't even remember. Some of the stuff that you guys have seen me -- the state I've been in?"
Ford said again he is not an addict or an alcoholic.
"If I had I problem, I'd be the first one to say I'm not fit to run the city," he said Tuesday. "Have I drank a little too much at times? You're absolutely right. Am I going to curb that? Absolutely I'm going to curb that."
Toronto City Councilwoman Jaye Robinson said the substance abuse is "affecting [Ford's] judgment," and said the episode has made Toronto "the laughingstock of North America if not the world."
Toronto police said they would not comment on Ford's admission, the Star reported.