The Toronto mayor, Rob Ford, has admitted during a heated city council debate that he bought illegal drugs while in office – but adamantly refused to step down despite calls from nearly every councillor to take a leave of absence and get help.

"I'm most definitely keeping this job," the 44-year-old Ford said, insisting he was "a positive role model for kids".

The mayor made the admission under questioning by a councillor and former ally, Denzil Minnan-Wong. Ford publicly has acknowledged that he smoked crack cocaine while in a "drunken stupor" last year but his comments on Wednesday marked the first time he admitted buying illegal drugs.

Ford paused for a long time after Minnan-Wong asked him if he had bought illicit narcotics in the past two years. Eventually he replied: "Yes I have."

"I understand the embarrassment that I have caused. I am humiliated by it," Ford said.

But he was defiant, saying he was not an addict and rebuffing suggestions from council members that he seek help. "I am not leaving here," Ford said. "I'm going to sit here and going to attend every meeting."

Moments earlier all but two of the 43 councillors present for the debate voted to accept an open letter asking Ford to step aside. Most of them stood up to urge the mayor to take a leave of absence.

It was a stark demonstration of his political isolation but the vote was merely symbolic because the city council does not have the authority to force the mayor from office unless he is convicted of a crime.

"Together we stand to ask you to step aside and take a leave of absence," councillor Jaye Robinson said, reading the open letter.

The packed council chamber erupted with applause when Robinson ended her speech saying: "Let's get on with city business."

Ford later tried to move a motion directing all council members to undergo "hair drug and alcohol testing" by 1 December but the council chair quickly ruled the motion out of order.

Ford then suggested that many council members were on drugs and they all knew stories about each other. But he added: "I'm not a rat."

Outside city hall hundreds of protesters chanted "Resign!" while organisers of Toronto's Santa Claus parade asked that Ford not walk in the procession this year.

Ford's refusal to step down has confounded the council, where many members agree that his erratic behaviour – from public drunkenness to threatening to kill someone in a videotaped tirade – has consumed Toronto's politics and undermined efforts to tackle other challenges.

But with no clear legal path to force him out the council is grasping for ways to shunt him aside and govern without him until next year's municipal elections.

The open letter was separate from a non-binding motion, also being debated on Wednesday, that would formally call on Ford to take a leave of absence, apologise to Toronto residents for misleading them and co-operate with police. The council voted 37-5 to ask Ford to take a leave of absence on that motion.

The deputy mayor, Norm Kelly, a Ford ally, announced shortly before the debate that he would support the motion, introduced by Minnan-Wong.

"I'm publicly advising the mayor to take some time," Kelly said.

One Ford ally, councillor Giorgio Mammoliti, called the motion a waste of time. "We can't tell him what to do. Only the electorate can tell him what to do," Mammoliti said.

Toronto police said in October they had obtained a long-sought video of Ford apparently smoking from a crack pipe but that it did not constitute evidence to charge him. Toronto police spokesman Mark Pugash said Ford's acknowledgment on Wednesday that he bought illegal drugs would be passed on to investigators.

News reports of the crack video's existence first surfaced in May but it has not been released publicly.

Another proposed motion would curtail Ford's powers, suspending his authority to appoint and dismiss the deputy mayor and his executive committee, which runs the budget process. It likely will not be debated until Friday.

Toronto's mayor already has limited powers compared with the mayors of many large cities in the neighbouring United States. He is just one voting member in the council and his power stems mostly from his ability, as the only councillor elected by citywide vote, to build consensus and set the agenda. That authority, many council members say, has evaporated in the crack scandal.

Ford was elected three years ago, riding a backlash from suburbanites who felt alienated by what they deemed Toronto's downtown-centric, liberal-dominated politics.

Despite his eroding political leverage, Ford has promised to seek re-election. He maintains a hardcore of supporters he refers to as "Ford Nation" who applaud him for abolishing an annual $60 vehicle registration tax, squeezing concessions out of the labour unions and other cost-saving measures.

More revelations about the mayor's misdeeds surfaced on Wednesday when a judge released documents from a drug case against a friend and occasional driver of the mayor, Alexander Lisi. Previously released documents revealed the mayor's ties and covert meetings with Lisi.

The police interviews with Ford's staffers reveal their concerns about the mayor's drug abuse and drunk driving, with one staffer alleging he saw Ford "impaired, driving very fast" and frightening a female staffer who was in the car with him.

In another incident Ford was described by a former chief of staff as being "very inebriated, verbally abusive and inappropriate with" a female staff member on St Patrick's Day. Another former staffer reported seeing the mayor drunk in his office about 15 to 20 times in the year he worked for him.

Earlier on Wednesday Ford was grilled by councillors about his links to a Toronto home where he was photographed with three suspected gang members. A police informant has described the residence as a "crack house" and police have said it relates to the crack video.

"That is not a crack house," Ford said. "Have you been in that house?"

Councillor Michael Thompson retorted: "I have no interest in being in that house. I am not a crack user."