Judy Lindsay says Ms Williams hosted an online meeting with her and two other families who's loved ones had been killed in accidents caused by drink-drivers hours before the mayor crashed her own car into a tree east of Brisbane on Thursday night.

Ms Williams says she'd had "several glasses of wine" before the crash, and admits it was a mistake getting behind the wheel but refuses to resign, saying it would be a "rash decision".

Police are investigating the incident and no charges have been laid.

Ms Lindsay, whose daughter Hayley was killed in a crash involving a drink-driver in 2009, says the mayor rang her in tears on Friday night to apologise.

"I just said I can't have any contact with you any more. You can't be doing the job you're doing. I trusted you and this is what you've done," Ms Lindsay told Nine's Today program on Monday.

"She's got to go, she's got to go, she has no respect for anybody in this community by doing what she's done.

"And if, you know, having a meeting with us, a Zoom meeting with us, wouldn't that stop you from getting in the car drunk and driving half an hour after having a meeting with us."

Queensland Opposition Leader David Crisafulli said his Liberal National Party colleague should face consequences for her actions.

"I have zero tolerance for drunk-driving, and it doesn't matter who you are, it doesn't matter what you do, it doesn't matter where you live: you should never put yourself in that position," he told reporters on Monday.

"And there has to be consequences for actions."

Premier Annastacia Palaszczuk refused to be drawn on the mayor's political future but did say it was very serious - particularly for someone who had campaigned on the issue.

"She was a very strong advocate against people drink driving," the premier told reporters.

"That's a matter for her now to have to think about what she's been campaigning about and the consequences of that."

Federal Opposition Leader Peter Dutton and Nationals leader David Littleproud, along with state Environment Minister Meaghan Scanlon and fellow Labor MP Don Brown have all called for Ms Williams to resign.

Mr Littleproud said the mayor's position was untenable, given her advocacy for the victims of drink-drivers.

"We know you're in public office, we know you don't always get it right, and I don't always get it right, but this is a big miscalculation ... I think her position is untenable," he told Today.

"I would hope she would do that under her own volition."

Mr Peter Dutton said drink-driving was "completely unacceptable" and Ms Williams needed to set a strong example "in terms of actions, accountabilities and consequences".

"My message, particularly as a former police officer, is to not have that extra drink. Don't drink and drive. I mean, there's no excuse for it, and the consequences can be deadly," he told reporters on Sunday.

Australian Associated Press