Gordon Matheson, who is openly gay, has issued a public apology and revealed he had been having a secret affair after being caught by police performing a sex act on another man in public.
This morning the 46-year-old Labour politician arrived as usual at his office in the City Chambers. A council source said: "It's business as usual. He's at his desk."
Mr Matheson, who represents Merchant City, faced calls today to resign after he was caught in a car near his home in the city's South Side with another man on December 12.
Both were questioned by police but no legal action is being taken following the incident in the Cathcart area. The Crown Office says there is "insufficient evidence" to prosecute either man.
There have been reports that a 38-year-old man involved was a former lover even though Mr Matheson lives with civil partner Stephen Wallace. They have been together for the last six years.
In a statement Mr Matheson said: "I have been having an affair. I have not lived up to my own standards and my loving partner deserves much better. I am sorry for the hurt and embarrassment this has caused and I will do all I can to make up for it."
His apology did not appease Tory councillor David Meikle. He said: "He has got to go."
Councillor Meikle believes the latest revelation follows a number of recent decisions which have left opposition politicians questioning Mr Matheson's judgment.
He added: "I think the public will be shocked and outraged about this. But this is not about what happened but is all to do with his lack of judgment. His Labour colleagues should show some leadership and take immediate action."
There's speculation that won't happen with opposition politicians today claiming no other senior Labour councillor wants the job.