Elon Musk rolled out some of his free-wheeling free speech on Wednesday, teeing off on Donald Trump's nascent social media platform, Twitter executives and censorship.

"Truth Social (terrible name) exists because Twitter censored free speech," Twitter's new owner-in-waiting tweeted to his 86.7 million followers on Twitter. "Should be called Trumpet instead!"

Musk did note, however, that the former US president's Truth Social platform, which launched in February, is currently ahead of Twitter and TikTok on the Apple Store when it comes to most downloaded apps.

NBC News, however, in a review of rankings from the Apple App Store and the Google Play store on Wednesday did not find Truth Social among the top 200 free and paid apps. But other sites, including Apptopia, an analytics company, did have it at No 1.

When Musk, the richest person in the world, sealed the deal to buy Twitter after the San Francisco company's board accepted his offer of $44 billion on Monday, many wondered if Trump would return to the platform after he was banned from the site following the Jan 6 storming of the US Capitol.

But Trump said Monday that he would not be back.

Musk's purchase, which still must be approved by Twitter's shareholders, has ignited perhaps the hottest meme-fest in social media history, with those on the right gleefully celebrating the pending change in ownership, while on the left, there is consternation and hand-wringing.

A regular refrain by left-leaning Twitter users when conservatives complained about censorship was how Twitter was a "private company", and they should look elsewhere.

Twitter is a private company in the sense that it isn't a government outlet, but its shares are traded on the New York Stock Exchange. Now, Twitter would literally become a private company under Musk.

"For Twitter to deserve public trust, it must be politically neutral, which effectively means upsetting the far right and the far left equally," Musk, 50, the CEO of Tesla and SpaceX tweeted Wednesday.

His pinned tweet from Tuesday says: "By 'free speech', I simply mean that which matches the law. I am against censorship that goes far beyond the law. If people want less free speech, they will ask government to pass laws to that effect. Therefore, going beyond the law is contrary to the will of the people."

Musk also poked The Washington Post, which is owned by fellow billionaire Jeff Bezos, founder of Amazon.com.

"The Washington Post targets me relentlessly!" Musk tweeted. "Their insults could be higher quality, but some are not bad. I gave them 3 stars on Yelp."

As part of the acquisition deal, Musk is prohibited from saying negative things about Twitter and its employees.

But in one message posted Tuesday afternoon, Musk, in response to a tweet about Vijaya Gadde, Twitter's chief legal officer, wrote, "Suspending the Twitter account of a major news organization for publishing a truthful story was obviously incredibly inappropriate."

Musk was referring to the New York Post's story in October 2020 about information found on a laptop computer that was left behind at a Wilmington, Delaware, repair shop by Hunter Biden.

Former Twitter CEO Dick Costolo responded directly to a second Musk tweet, accusing him of bullying over the comments on Gadde.

"What's going on? You're making an executive at the company you just bought the target of harassment and threats," Costolo wrote.

A filling Tuesday with the Securities and Exchange Commission that details Musk's purchase of Twitter says that while he "shall be permitted to issue tweets about the merger", his tweets cannot "disparage the company or any of its representatives".

Twitter CEO Parag Agwaral also seemed to be referring to Musk in a tweet Wednesday.

"I took this job to change Twitter for the better, course correct where we need to, and strengthen the service," Agwaral wrote. "Proud of our people who continue to do the work with focus and urgency despite the noise."

Musk continued to tweet into Wednesday evening.

"Attacks are coming thick and fast, primarily from the left, which is no surprise, however I should be clear that the right will probably be a little unhappy too," Musk tweeted around 6 pm EDT. "My goal is to maximize area under the curve of total human happiness, which means the ~80% of people in the middle."