Former United States president Donald Trump vowed he would not be returning to Twitter if his account was reinstated following the purchase of the platform by .
Mr Trump said he would be using his own site, Truth Social, although he appears only to have posted once since its launch in February.
"I am not going on Twitter, I am going to stay on Truth," Mr Trump said, according to FoxNews.com, adding that Mr Musk was a "good man" who would improve the service.
"We're taking in millions of people, and what we're finding is that the response on Truth is much better than being on Twitter. Twitter has bots and fake accounts, and we are doing everything we can," he told the network.
Mr Trump was — and impeached for a second time — following the by his supporters, with the company citing the "risk of further incitement of violence".
The California-based platform has been dogged by complaints from conservatives that it was biased against them and violating their free speech rights with suspensions for rule-breaking.
Politicians have called for the modification or repeal of a 1996 law shielding social media platforms from liability over their content moderation practices and for the postings of third parties.
Mr Musk, whose wealth stems from the popularity of Tesla electric vehicles, as well as other ventures, struck a deal Monday to buy Twitter for US$44 billion ($61 billion), the company announced.
The publicly traded firm will now become a private company owned by Mr Musk, who negotiated a purchase price of US$54.20 ($75.50) per share, Twitter said.
"Twitter has a purpose and relevance that impacts the entire world. Deeply proud of our teams and inspired by the work that has never been more important," the company's CEO Parag Agrawal said in a tweet.
Musk, a self-proclaimed "free-speech absolutist," is , and analysts have speculated that he may reinstate accounts of Mr Trump and allies who have fallen afoul of the rules.
"Free speech is the bedrock of a functioning democracy, and Twitter is the digital town square where matters vital to the future of humanity are debated," Mr Musk said in a statement released by Twitter on Monday.
"I also want to make Twitter better than ever by enhancing the product with new features, making the algorithms open source to increase trust, defeating the spam bots and authenticating all humans."
Mr Trump appeared to have spoken to Fox News before he was aware of Musk's purchase. But progressive group Media Matters for America had already warned that the former president could return.
"Any negotiations to sell Twitter to Musk must include clear enforceable mechanisms to uphold and maintain existing community standards, including the removal of those who violate those standards," the group's president Angelo Carusone said in a statement.
Mr Trump struggled to pronounce the name of his social media platform during a rally in Ohio on Saturday, appearing to refer to it as "something called trove, Truth Central."
He took several weeks to post after its launch in February.
More than one million users downloaded the app after its launch but interest appears to have waned amid technical glitches and long wait times to access accounts.
Mr Musk, who has complained of overzealous moderation on the platform, earlier in April, then offered to buy the whole company outright, citing a mission of preserving free speech.
While the firm's board initially said it was reviewing his offer, it later rebuffed him and adopted a "poison pill" plan that would have made it harder for Mr Musk to acquire a controlling position.
Last week, the billionaire said he had lined up financing. Despite his wealth, the question of financing had been seen as a potential stumbling block because much of his holdings are in Tesla shares rather than cash.
In a filing, Musk had pointed to a US$13 billion ($18 billion) debt facility from a financing consortium led by Morgan Stanley, a separate US$12.5 billion ($17.4 billion) margin loan from the same bank, as well as US$21 billion ($29 billion) from his personal fortune as being behind the deal.
His efforts have raised hopes about the commercial potential of Twitter, which has struggled to achieve profitable growth despite its influential spot in culture and politics.
Under Mr Agrawal, who took over as Twitter CEO late last year, the company has made progress on new monetisation features, such as subscription products, Truist securities said in a note, adding that "short term, Mr Musk's involvement at this stage runs the risk of disrupting those efforts."