Alan Blumenthal, one of the 42-strong Tory group on Birmingham City Council, called on Bernard Zissman, the group's leader, to 'consider your position' after an embarrassing walkout in the council chamber.
Mr Blumenthal later retracted the demand, made in a letter leaked to the Labour Party, and said he fully supported his leader.
The city's Conservatives started out with high expectations of winning control of England's second city. But following a poor start to the campaign, they face an uphill struggle.
An unhelpful recent party political broadcast by the Tories was widely interpreted as an attack on the city of Birmingham itself, not its Labour administration.
Labour performed well in the 1990 local elections and is defending 28 of the 39 seats to be contested this year, many of which were won from the Conservatives for the first time four years ago. The Conservatives need a swing of 5 per cent from Labour's 1990 result to take control.
Mr Blumenthal admitted he acted on the spur of the moment following last week's council meeting in which Mr Zissman led a walkout over Labour's attempts to stall a debate over education.
His letter, which was due to be circulated to all Conservative councillors, said: 'I, as did other members of the group who remained in the chamber, felt distinctly embarrassed by your actions and, of course, the Labour Party took great amusement at highlighting this.
'I hope that this is a lesson to you not to act with such haste in the future and possibly you should consider your position as leader.'
Mr Zissman was unavailable for comment.Reuse content