British Prime Minister Keir Starmer on Wednesday warned that the BBC should "get their house in order" after US President Donald Trump said he had an "obligation" to sue the corporation for $1 billion over a misleading speech edit.

Speaking in parliament, Starmer said that while he supports a "strong and independent BBC", he also believed it should "uphold the highest standards to be accountable and correct errors quickly".

"Where mistakes are made, they do need to get their house in order," he said in response to a question calling for him to urge Trump to abandon his legal threat.

Trump's lawyers threatened the British broadcaster with a billion-dollar lawsuit on Monday, according to a letter seen by AFP, as the BBC apologised for giving the impression the president had urged "violent action" ahead of the 2021 assault on the US Capitol.

Later, in a Fox News interview, which was recorded Monday, Trump was asked if he planned to sue the BBC.

"I guess I have to, why not?" said the president in his first public comments on the potential for legal action.

"I think I have an obligation to do it because you can't allow people to do that," Trump said, without confirming whether he had officially begun proceedings to file a defamation lawsuit.

"They defrauded the public and they've admitted it."

Britain "is supposedly one of our great allies," and "the government has a chunk of that one," Trump added, referring to the publicly funded BBC.

Starmer's Labour government has been performing a tightrope act between backing the broadcaster's independence without seeming to take a side against Trump.

The BBC director-general and the organisation's top news executive resigned Sunday over the controversy.

The BBC has said that it would "review" the letter from Trump's legal team. BBC chair Samir Shah issued a public apology on Monday for an "error of judgment" made in the editing.

Fifty-seven percent of Britons believe the BBC should apologise directly to the US president, according to a YouGov poll published on Tuesday. But a quarter were against such an apology. 

The row comes at a politically sensitive time for the BBC, which is due to renegotiate the Royal Charter that outlines the corporation's governance. Its current charter will end in 2027.

Trump has been accused of launching a number of lawsuits to stifle criticism in US media since returning to power in January.

The BBC documentary featuring the edited Trump speech was aired last year.

It appeared he had told supporters he was going to walk to the US Capitol with them and "fight like hell," but he also told the audience in the intervening period: "We're going to cheer on our brave senators and congressmen and women."