Chris Heaton Harris tweeted on Wednesday night about his concerns of the spread of fake news after false reports emerged he had resigned from the cabinet.
Mr Heaton-Harris described these reports as "utter tosh" and tagged Mr Musk, saying that he hoped the tech billonaire would "eliminate fake news on Twitter".
Mr Musk replied just after 8am asking: "What does a tosh look like?"
The Telsa owner has used his personal account to respond to comments about his tenureship at Twitter over the past few days.
After public confusion yesterday over the launch of "official" tags alongside the new "Twitter Blue" service, Mr Musk responded to tech Youtube star Marques Brownlee saying "I just killed it."
He added: "Blue check will be the great leveler."
Twitter is preparing to allow any user to sign up for a blue-tick verification badge by subscribing to the Twitter Blue service and paying $8 (£7) a month. But the move has been controversial, with some concerned it will make it harder to identify authentic accounts on the site and could lead to more misinformation. With Musk reportedly planning to bring back banned accounts such as Donald Trump's, a number of celebrities have said they will no longer use the platform, including model Gigi Hadid, who described it as a "cesspool of hate and bigotry". Other celebrities like Stephen Fry and Whoopi Goldberg also said they are leaving.
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