Ford said it is "unfortunate that the word I did not say has been ascribed to me by the media but I wish to sincerely apologize."
Reporter Daniel Dale served Ford with a libel notice last week, demanding Ford apologize.
Ford, who admitted last month to smoking crack "in a drunken stupor," appeared on a Vision TV interview and accused Dale of taking pictures of his little kids. Ford said he didn't "want to say that word but you start thinking what this guy is all about."
Ford's insinuation was related to an instance when Dale was close to Ford's house in May 2012, investigating a plot of public land adjacent to Ford's home that the mayor wanted to buy.
Dale has said he was writing a story about the plot so he went to take a look at it when the mayor emerged from his home to confront him. Dale said he didn't take any pictures and said the mayor's two children were nowhere in sight.
"I did not mean to insinuate anything about Mr. Dale personally in my interview," Ford said in prepared remarks in City Council. "I certainly did not intend to suggest that he is a pedophile. I was merely commenting on the thoughts that went through my mind on the night."
Dale said on Twitter that Ford's apology was unsatisfactory.
"I asked Mayor Ford to 1) retract all of his false claims about my conduct and 2) issue an unreserved, abject, complete apology," Dale tweeted.
"In his "apology," the mayor didn't retract anything at all. Instead, he blamed the media for its reasonable interpretation of his words."
Ford has rebuffed intense pressure to resign over his admitted crack use and revelations of other erratic behavior. The Toronto City Council has stripped him of most of his powers in an attempt to sideline him but the conservative mayor has vowed to seek re-election next year.
The bombastic mayor has not shied from the limelight. During a council session Tuesday, Ford danced vigorously to a band playing "One Love" on the chamber floor—around the same time that Dale was sending his Twitter messages.
Ford has said he has quit drinking alcohol and is exercising daily after having a "come to Jesus moment."
His lawyer, Dennis Morris, said Ford has lost 26 pounds (12 kilograms) in the last five weeks. The mayor weighed himself in his office Tuesday and found he was down to 310 pounds (140.6 kilograms), said Morris, who was at City Hall to pick up some bobblehead dolls of Ford to give as Christmas gifts. The mayor has signed some of the bobbleheads for charity.
Ford has taken pointed shots at the media, calling journalists maggots. Allegations about Ford smoking crack surfaced in May when two reporters for the Toronto Star and one from the U.S. website Gawker said they saw a video of Ford appearing to smoke from a crack pipe, but they did not obtain a copy. Ford vilified the Star, accusing the paper of trying to take him down.
Ford first denied the tape existed but later when Toronto police announced in October they had obtained a copy, the mayor admitted he had smoked the drug.
Ford lashed out at Dale's bosses at the Toronto Star on Tuesday, saying they put him and Dale in this situation
Toronto City Councilor Shelley Carroll called Ford's apology "insincere."
"He's an expert at non apologies. He's been doing it for years. A real apology is 'I caused you harm Daniel, I am sorry for that,'" Carroll said. "You'll never get an admission of guilt from Mayor Ford. It's not his style and it hasn't been since birth."