A total of 72 MPs wrote to the director-general claiming Leave voting constituencies had their views “unfairly represented” by the BBC.
He said: “I have to be careful because I am a journalist, not an editor, I write a column for the Times, so I'm always a wee bit weary about criticising others in my profession.
“But there is a very good point behind this letter, that there is a mindset, and I won’t single out the BBC, but there is a mindset among some who see Brexit as a catastrophe, and who look at any bit of good news we have as occurring despite Brexit.
Michael Gove argued that Brexit voters deserved respect
“Any news outlet should bear in mind that 17.4 million voted to Leave.”
The Conservative MP continued arguing that licence payers or readers of media organisations did not deserve to be insulted because they voted to leave the European Union.
He added: “These people [voted to Leave] after an intense debate after listening to the arguments and whether these people are licence payers, or readers, then I think that they deserve respect,” he said.
“I think that means thinking hard about balance and objectivity, but as I say I don’t want to single any individual organisation out.”
The complaint was mainly signed by Conservative MPs, however three Labour MPs, eight DUP MPs and Ukip’s only MP, Douglas Carswell, also added their names.
Any news outlet should bear in mind that 17.4 million voted to Leave
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The letter suggested that the BBC had become “partisan” and had fallen “far short” of providing balanced coverage.
It read: “We know many Leave-voting constituencies have felt their views have been unfairly represented.
“This phenomenon is weakening the BBC's bond with the 52 per cent who voted Leave and all who wish to make a success of the decision made.
“The BBC has a much larger market share than any newspaper – it runs the most-used news website in the country, on top of its television and radio coverage.
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“This, as well as viewers' belief in its neutrality, means that BBC bias can have a substantial effect on the national debate.
“We are therefore asking you to take steps to correct these flaws in the BBC's coverage of our EU exit at the earliest moment.”
A BBC spokesperson said: “While we are always live to our critics and understand that passions are running high on all sides of the debate, it is the job of the BBC to scrutinise and analyse the issues on behalf of the public and to hold politicians to account across the political spectrum.
“That is what the BBC has been doing. It is what the BBC will continue to do. It is precisely because of this, that the public trusts the BBC.”