Tory group leader Andrew Eade stormed across the council chamber to confront Labour rival Clive Elliott and told him: "We can sort this out outside."
Councillor Elliott, a member of the Labour Cabinet on Telford and Wrekin Council, had said: "What does he do for his Special Responsibility Allowance?
"Even the seven dwarves went out to work. I can see some of them here: Sneezy, Sleepy, Dozy, Happy, Doc and Bashful.
"What I don't see is any leadership from Grumpy."
Councillor Eade said to mayor Kevin Guy, chair of the meeting: "Either you shut him up or I will" before getting up to stand next to Councillor Elliott.
He said: "Do you want to come and talk about it outside? Come on. We can sort this out outside."
Councillor Elliott kept his seat and replied: "No, you go outside and let me know how you get on."
Councillor Elliot said later: "I am too distressed to think about the terrible incident.
"I need to consider what to do in the morning."
He added: "I am alarmed, harassed and distressed by the episode."
Speaking this morning, Councillor Eade dismissed the argument as 'something and nothing'.
"I just wanted to talk to him to point out the error of his ways," he said.