Ms Short is back in the spotlight again
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Clare Short made a "significant error of judgement" over her repeated attacks about the Iraq war, said Ian McCartney.
But the Labour chairman told the BBC that no-one was trying to "silence" his former cabinet colleague.
Ms Short has been under fire for saying Britain spied on UN secretary general Kofi Annan.
Her remarks prompted her to be called in for a dressing down by Labour's Chief Whip Hilary Armstrong.
Mr McCartney's comments coincide with a meeting of Labour's parliamentary committee, whose membership includes Tony Blair and John Prescott.
Error?
He told BBC Radio 5 Live: "Nobody is attempting to silence her. She makes that choice, she has made the choice.
"I think it is an error, a significant error of judgment, but that is for her. She is a mature politician."
Labour confirmed that Ms Armstrong had "updated the committee and also said she would be reporting back to a future meeting".
Mr McCartney added Ms Short "was a politician who was in the Cabinet that voted for the war, she was in the Cabinet that agreed the strategy of the United Nations and that strategy is now seen to be a successful one."
He has already said that Labour would not take any action that would turn the former international development secretary into a martyr.
Last week Ms Short said "little of the intelligence" she saw in government "seemed particularly useful" and she accused the heads of all three of Britain's intelligence services of "going native with No 10" in the run up to war.