Speaking on his weekly radio show on Sunday, Ford brushed off the scandal, calling the media a "bunch of maggots," and promised to run in the next election.
"I'll be the first putting my name on that ballot," he said.
Ford apologized for his maggot comment on Monday.
The drug-use allegations are the latest in a string of scandals for the mayor, who has been chided for ignoring city work to coach high school football and was briefly ordered out of office last year after he was found guilty of conflict of interest.
The latest controversy does not appear to have hurt Ford's popularity, according to a Forum Research Inc poll released over the weekend, although he is at risk of being ousted in a 2014 election.
The poll, taken on Friday after Ford denied the drug-use claims, found the mayor would still lose a one-on-one battle for his job if pitted against Olivia Chow, a former city councilor and current federal member of Parliament widely touted as a candidate.
It showed Ford would get 36 percent of the vote, in line with a May 10 poll taken before the latest scandal broke, while Chow would get more than half the vote.
The mayor's popularity has been attributed to the support of the "Ford Nation," suburban voters who pushed Ford into the city's top office in 2010 and back his agenda of cutting taxes and reducing city spending.
"Rob Ford is really both the Teflon and Kevlar Mayor - nothing sticks to him and nothing penetrates his armor," Forum Research founder Lorne Bozinoff said in a statement.
"His recent troubles have had absolutely no effect on his electoral prospects."