The experienced Wesminster journalist also faced an online petition last year calling for her to be sacked. It was eventually shut down by 38 Degrees, the campaign group hosting the petition, after executives said it had been “hijacked, and used as a focal point for sexist and hateful abuse” of Ms Kuenssberg.
Sir David told the Royal Television Society Convention in Cambridge: “It is the responsibility of our journalists to ask the question – even if it is direct, awkward or unwelcome.”
At one event in during the election campaign in May, Mr Corbyn attempted to call off his supporters after they targeted a Channel 5 reporter with boos.
The Labour leader said: “Journalism and journalists are intrinsic to a democracy and a free society.”
There have also been incidents of booing and intimidation of journalists at Ukip events.