Asked about the decision to add a label to the BBC's main Twitter account describing it as "government funded media", Mr Musk said: "I know the BBC is generally not thrilled about being labelled state media."
Earlier this week, the corporation contacted the social media giant over the designation on the @BBC account to resolve the issue "as soon as possible".
"The BBC is, and always has been, independent. We are funded by the British public through the licence fee," it said.
Mr Musk said Twitter was adjusting the label for the BBC to "publicly-funded".
"We're trying to be accurate," he said.