US President Donald Trump said on Friday he would sue the BBC for up to $5 billion, after the British broadcaster apologised but said it would not pay damages for a misleading speech edit.

The broadcaster has rejected Trump's legal defamation claim, but the president appears determined not to let the matter rest, even after the departure of top BBC executives.

"We'll sue them for anywhere between a billion and five billion dollars, probably some time next week. I think I have to do it. They've even admitted that they cheated," Trump told reporters aboard Air Force One.

Trump earlier said he would sue the BBC for $1 billion, an already enormous sum that represents 13 percent of the organisation's annual revenue.

The broadcaster has been in turmoil since the edited clip from its flagship news program "Panorama" -- aired before the 2024 presidential elections -- resurfaced last week.

On Monday, the BBC apologised for giving the impression in the documentary that Trump had directly urged "violent action" just before the assault on the US Capitol by his supporters on January 6, 2021.