Ukip chairman Steve Crowther has urged the party's only MP to keep his "very unhelpful" public calls for a change of leadership behind closed doors.
Douglas Carswell's demand for a "fresh face" at the head of the party drew a "put up or shut up" retort from leader Nigel Farage, who hinted that the ex-Tory's future in Ukip was under threat.
Mr Crowther said the Clacton MP was "absolutely wrong" to suggest that a disappointing result in the Oldham by-election showed Mr Farage had taken the party as far as he could.
And he told the BBC Radio 4 Today programme that the row would be discussed when the party's National Executive Committee - on which both the politicians sit - meets next month.
"This is very unhelpful. As a party chairman it is not something I relish," he said.
"There is a time and a place to have discussions about the leadership of the party but I don't think that on theeve of an EU summit or on the BBC is either of them.
"This news was released on the day we were celebrating the utter collapse of the Prime Minister's negotiating position in Europe."
Political life was "not without its speed bumps", said Mr Crowther, but the party was in good shape.
"Broadly speaking we are continuing to progress: we took control of a council; we had four million votes in the general election; our poll ratings are holding up since the general election against all predictions.
"Political life is not without its speed bumps."
Asked what he thought were the motivations for Mr Carswell - who insists he does not want the leadership, Mr Crowther said: "Douglas is an independent thinker. It's his principal characteristic as a politician.
"He is just voicing his view.
"But, as I said, musing aloud is all very fine and dandy but it's not very helpful if you are trying to maintain some sort of party direction and discipline."
He went on: "All political parties have conversations about how it's going. But these are things that ought to be held within the party.
"Douglas is a member of the National Executive Committee and the NEC will be wanting to speak to him about this in January.
"They will be wanting to talk about the thing we want to do, which is to run a really coherent and cohesive campaign to leave the European Union.
"And this has been going very well. The polls are moving in our direction."