Labour Party Councillor David Wright - Telford & Wrekin Council's cabinet member for economy, housing, transport and infrastructure - faced calls to step down from the rival Conservative group members after a comment made to its leader Nigel Dugmore.
The incident came during a meeting of full council, and a discussion on a motion from Councillor Wright expressing concern over plans for government changes to planning policy.
He accused Councillor Dugmore of attacking council officers and not him directly because "you know you will get a whack".
Councillor Dugmore said he was "disappointed that Councillor Wright felt the need to threaten me with physical violence", and called on the former Telford MP to resign.
In response Councillor Wright apologised and added: "I obviously meant whack him in debating terms."
Councillor Wright's comment which sparked the incident was: "Yet again you have used a meeting of this council to attack council officers who have no opportunity whatsoever to respond to your remarks.
"You can attack me Councillor Dugmore but you don't seem to want to do that because you know you will get a whack and what happens is you go for the officers Councillor Dugmore, who cannot respond to you."
It is understood Telford & Wrekin Council leader Shaun Davies is not considering asking his cabinet member to resign.
Councillor Dugmore said: "I am very disappointed that Councillor Wright felt the need to threaten me with physical violence. It is my civic duty to hold officers and councillors to account.
“This is no way for a councillor or cabinet member to act and he should do the right thing and resign.”
He added: “If Councillor Wright doesn’t do the right thing and resign then his boss, Councillor Shaun Davies Leader of Telford & Wrekin Council should sack him before he brings anymore embarrassment to the office he holds.
“We have also written to the monitoring officer at Telford & Wrekin Council lodging a formal complaint that Councillor Wright has broken the code of conduct."
Councillor Wright said that looking back on the debate he should have used different language.
He said: “Councillor Dugmore continues to attack council officers in debate and they aren’t able to respond. I obviously meant whack him in debating terms – however on reflection it would have been better not to use the figurative debating comment I did and I apologise accordingly.”
A spokesperson at Telford & Wrekin Council said: “Correspondence has been received by the monitoring officer. This will now be considered. In these cases, the monitoring officer will consult with an independent person who will consider if the complaint is politically motivated and whether or not it is in the public interest to pursue. A decision will be made in due course and the appropriate action taken following consultation with the independent person.”