Some members of Friday’s Question Time Leader’s Special audience laughed when a woman asked Mr Johnson: “How important is it for someone in your position of power to always tell the truth?”
The corporation faced accusations of bias after the laughter was edited out of this clip in its Saturday lunchtime bulletin.
It prompted a growing storm over the weekend and Monday, with the Mirror reporting the Liberal Democrats had written to media watchdog Ofcom demanding an investigation.
The BBC, having faced three days of calls to apologise, did so on Monday afternoon.
A spokesperson said in a statement: “This clip from the BBC’s Question Time special, which was played in full on the News at Ten on Friday evening and on other outlets, was shortened for timing reasons on Saturday’s lunchtime bulletin, to edit out a repetitious phrase from Boris Johnson.
“However, in doing so we also edited out laughter from the audience. Although there was absolutely no intention to mislead, we accept this was a mistake on our part, as it didn’t reflect the full reaction to Boris Johnson’s answer.”
It added: “We did not alter the soundtrack or image in any way apart from this edit, contrary to some claims on social media.”
Mr Johnson had been taking part in the special debate in Sheffield which featured the leaders of the four main political parties.
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During the programme, in which each leader was quizzed for half an hour by audience members, the Prime Minister also refused to apologise over his use of language and defended Tory austerity in the programme.
As well as laughter, Mr Johnson also faced groans from the audience when he said the NHS’s demands could only be met when “we get Brexit done”.
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