Mr Musk purchased Twitter for $44 billion last week, after a confusing series of events that made him the company’s largest shareholder and future board member, before stepping down from the board seat and offering to buy the company outright.
"It’s a free country,” Mr Musk told reporters at the Met Gala on Monday.
"Certainly if anyone doesn’t feel comfortable with that, they will on their own accord go somewhere else. That’s fine," he said.
Mr Musk has already publically criticised Twitter employees, including chief legal officer Vijaya Gadde, despite a clause in the deal that he cannot “disparage” the company or its representatives.
A Politico story claimed that Ms Gadde, who has been handling sensitive issues at Twitter like harassment and harmful speech, cried during a meeting about how the company could change under Mr Musk’s ownership.
Neither Ms Gadde nor Mr Musk responded to The Independent’s requests for comment. Twitter declined to comment to The Independent or define which of its employees count as its “representatives”.
Mr Musk also said that he wanted to increase the number of people using Twitter.
"Right now it’s sort of niche. I want a much bigger percentage of the country to be on it, engaging in dialogue," said Mr Musk, adding that it should be “as broadly inclusive as possible, where ideally most of America is on it and talking".
While Mr Musk’s purchase of Twitter would take the company private, it is unclear how long such a spell would last.
The billionaire has reportedly said he plans to stage an initial public offering of Twitter in as little as three years of buying it, according to the Wall Street Journal, in order to help garner funds for his purchase.
Private-equity firms often take companies private with the aim to make changes before taking them public again, and as such Mr Musk’s plan could help assure investors of Twitter’s future operations and profitability – although Mr Musk has not been specific about his plans.
Mr Musk reportedly suggested that websites should pay Twitter for embedding tweets in order to increase revenue for the social media service, although reports from the meeting said the Tesla and SpaceX chief was “thin on detail”.