Tom Gordon, who sits on Labour-run Wakefield Council, appeared to suggest that Cabinet member Matthew Morley had added his mother on the social networking site, at a full council meeting on Wednesday afternoon.
Coun Gordon, who is the Lib Dems' sole representative on the authority, made the remarks during questions to Coun Morley, who is portfolio holder for transport.
After asking about a pothole issue in his Knottingley ward, Coun Gordon added: "I was wondering, is it appropriate for a Cabinet member to be trying to add my mum on Facebook?"
Amid amused looks in the chamber, an apparently confused Coun Morley replied: "I have no idea. I don't know who your mum is."
Should sparring politicians add each other's family members on social media? The debate remains unresolved.
Local Democracy Reporting Service