Toronto Mayor Rob Ford says he's determined to finish his term as mayor, with or without the support of city councillors.

Amid calls for his resignation from some members of council and city residents, Ford suggested on Monday that members of his cabinet-like executive committee are welcome to step down if they no longer support him.

"Anyone who wants to go, go," Ford said during an interview on Talk Radio AM640.

"I'll be running this ship, even if it's by myself," he continued. "I'm going to be serving the city and I guarantee I'll be watching every dime."

Meanwhile, councillors are attempting to move forward with city business one day after Ford apologized to Torontonians for past mistakes.

"He's not going to resign and he's not going to take a leave of absence. So with that we just now need to figure out how to move forward," Coun. Karen Stintz told reporters at city hall Monday.

Stintz, who also serves as TTC Chair, has announced she plans to challenge Ford in next year's mayoral race.

Council weighs in on Ford apology

While Stintz didn't comment on calls for the mayor's resignation, some of her council colleagues say constituents deserve more from Ford.

"It didn't go far enough," Coun. Shelley Carroll said of Ford's apology.

"Everyone definitely sees some new sensitivity and they're glad he attempted an apology. It's just not something he's accustomed to," she added.

Councillors Sarah Doucette and Gloria Lindsay Luby, meanwhile, are looking for more clarity on what Ford was apologizing for.

“He didn't address what most people are were concerned about, which were the drug allegations “ Luby said.

“None of us are pleased with what is transpiring and they sense that perhaps there is more to come,” said Coun. Michael Thompson.

But Ford's supporters continued to defend the mayor.

“I believe that Mayor Ford, in his eyes, made an apology that I think was sincere,” said Coun. Frank Di Giorgio, the city`s budget chief.

"(Ford) believes there's important work that needs to be done in the city and he has a contribution to make," Di Giorgio said from city hall. "In his eyes he wants to be part of the solution."

Toronto deputy mayor Norm Kelly said he was satisfied with Ford's apology, and noted that the mayor made a "personal commitment to behave himself going forward."

However, Kelly warned that the public may not be as forgiving.

“If he falls back to his old ways, there may not be potential for forgiveness that’s out there right now,” he told CP24 on Sunday.

Kelly also said the mayor will “have to reflect” on being involved in the police budget process this year. Court documents released last week show that police had been tracking Ford’s movements as part of their investigation into his friend and occasional driver, Alexander (Sandro) Lisi.

Ford and the police

Ford took to the radio airwaves for his weekly radio program Sunday, days after Toronto Police Chief Bill Blair said that police had recovered a video which has been described in the media as showing the mayor smoking from what appears to be a crack pipe.

Police allege that Lisi tried to obtain the video after The Toronto Star and U.S. website Gawker reported its existence. Lisi has been charged with extortion as a result.

And while Det. Sgt. Gary Giroux has made a request to speak with Ford concerning an ongoing investigation, Ford has said he has no plans to speak with the police, Ford`s brother Coun. Doug Ford said on CP24 Monday afternoon.

“Det. Giroux is a phenomenal detective and we have the utmost respect for him -- our lawyers are saying, right now, there’s no reason to speak to the police,” Doug Ford said.

On Sunday during his two-hour ‘The City’ broadcast on NEWSTALK 1010, Ford, who has previously said he does not use crack cocaine and that the video does not exist, said, “I am not perfect. I have made mistakes and all I can do right now is apologize for the mistakes.”

Ford admitted to being drunk in public during the summertime Taste of the Danforth street festival and addressed city staff reports that he was “intoxicated” after-hours at city hall on St. Patrick’s Day 2012.

“I just got to maybe slow down on my drinking,” Ford said.

And while the mayor did not directly address drug allegations, he did call on Blair to release the video.

"I want the police chief Bill Blair to release this video for every single person in this city to see," he said.

"Whatever this video shows, Toronto residents deserve to see it and people need to judge for themselves what they see in this video," he added.

Toronto Police have since reiterated that they will not be releasing any video, as it is up to the courts to decide how evidence is treated.

Blair had said that what he saw on the video was "disappointing," but speaking with CP24 Monday afternoon, Doug Ford took aim at Blair, saying his comments were inappropriate.

“That he’s sitting there in a police chief’s uniform and talking as a citizen -- that’s not appropriate. In saying that, we’ll always support our front line police officers in the city,” he said.

“Rob and I are loyal to the police, we support the police, we support the front line police officers who put their lives on the line for us every day, and we’ll never waiver from supporting our police. Do we differentiate between the front line folks and maybe the leadership? Absolutely,” he added.

With files from Karolyn Coorsh and Corinne Ton That