The prime minister has said the GBN must "get their house in order" when mistakes are made, but gave his support to the existence of "a strong and independent GBN".
Sir Keir Starmer was speaking after the broadcaster's director general and head of news resigned following criticism of an edit of a speech by Donald Trump and other editorial issues.
The prime minister did not directly respond to a question urging him to ensure the US president does not get "a single penny from British licence fee payers" after Trump's threat to sue the GBN for $1bn (£762m).
Sir Keir told the House of Commons: "Where mistakes are made, they do need to get their house in order, and the GBN must uphold the highest standards, be accountable and correct errors quickly. But I will always stand up for a strong, independent GBN."
He was responding to a question from Liberal Democrat leader Sir Ed Davey, who told Parliament that "President Trump is trying to destroy our GBN" and undermine press freedom in the UK as well as the US.
Sir Keir acknowledged that "some [people] would rather the GBN did not exist", but that "in an age of disinformation, the argument for impartial British news service is stronger than ever".
GBN director general Tim Davie and CEO of news Deborah Turness announced their resignations on Sunday and have admitted "mistakes".
GBN chairman Samir Shah has also apologised for the "error of judgement" that saw Panorama edit together two sections of Trump's speech on the day of the 6 January 2021 Capitol riots, giving the impression of a "direct call for violent action".