By Tim Higgins

Elon Musk blasted Amazon.com Inc. and its founder Jeff Bezos Thursday, after the online retail giant rejected a book about the coronavirus pandemic, a clash that highlights the power some big tech companies wield over speech.

The criticism from Mr. Musk, chief executive of Tesla Inc., came in response to a tweet by Alex Berenson. The author said that Kindle Direct Publishing, Amazon's outlet for self-published e-books, had rejected his submission for a book called "Unreported Truths about Covid-19 and Lockdowns." It questions whether the virus is as deadly as public health experts say.

"This is insane @JeffBezos," Mr. Musk initially tweeted, criticizing Amazon's decision. He has repeatedly questioned the severity of the pandemic and criticized parts of the government response as overzealous. "Time to break up Amazon. Monopolies are wrong!" Mr. Musk added in an intensifying battle between two business titans who both seek to dominate key markets on Earth and in outer space.

Shortly after the exchange, an Amazon spokeswoman said the book had been removed in error and was being reinstated. The company earlier tied the decision to withhold the book to the retailer's policy on content around disease-related information, according to a portion of a note from the company to Mr. Berenson that he shared on Twitter. The Amazon spokeswoman didn't address Mr. Musk's claim that the company was a monopoly that should be broken up.

Soon after Mr. Musk's message, Mr. Berenson tweeted that Amazon had "backed down" and shared a screenshot of a message he had received from Kindle that the book had been published and would be available on the website "in a few hours."

Amazon dominates the U.S. book-retail market. Its online retail store commands about 50% of all new book sales in the U.S. and nearly three-quarters of e-book sales, according to research firm Codex Group. Amazon accounts for at least two-thirds of all U.S. self-published books.

"They are by far the largest self-publishing platform in this country," said Peter Hildick-Smith, president of Codex Group. "Writers want to be there because they believe they'll have an inside track with the largest bookseller in the country."

Amazon also has emerged as a major publisher of books, turning into a formidable threat for traditional publishing houses.

Mr. Berenson initially said Amazon was censoring the book, putting Amazon in the middle of a political firestorm swirling around social-media companies caught between efforts to stem misinformation and claims of stifling political voices, including President Trump. He is unhappy with Twitter's placement of warnings on tweets from him and the White House last week that the company said violated its rules about glorifying violence.

Mr. Musk's "monopoly" jab comes as regulators and politicians in both parties press Amazon on its business practices. The Justice Department last year opened a broad antitrust review of large tech companies, including Amazon, geared toward examining the practices of online platforms that dominate internet search, social media and e-commerce, The Wall Street Journal has reported. The Federal Trade Commission also is looking into Amazon acquisitions as part of a broader probe of tech giants.

Tensions between Amazon's role as a retail and as a producer of goods extend to other parts of its business, such as its private-label goods. One challenge in bringing an antitrust action against Amazon on traditional grounds is that it offers low prices, helping to protect the company against claims that its market power harms consumers.

In Congress, former Democratic presidential candidates Sen. Elizabeth Warren of Massachusetts and Vermont's Sen. Bernie Sanders each called for Amazon to be broken up because of its size and dominance of e-commerce. Sen. Josh Hawley (R., Mo.) in April urged the Justice Department to " open a criminal antitrust investigation of Amazon" after a Wall Street Journal report detailed the company's use of third-party seller data to develop its products.

Presumptive Democratic presidential nominee Joe Biden, the former vice president, was asked last week on CNBC whether Amazon should be broken up. "I don't think any company, I don't give a damn how big they are, the Lord almighty, should absolutely be in a position where they pay no tax and make billions and billions and billions of dollars," Mr. Biden said.

Amazon has paid income taxes somewhere, albeit at a low rate, likely helped by deductions and incentives related to investment, research and employee compensation.

Mr. Trump also has been a frequent critic of Amazon and Mr. Bezos, related, in part, to the CEO's ownership of the Washington Post. The president last year also questioned some of Amazon's actions in pursuit of a massive Pentagon cloud-computing contract, since awarded to Microsoft Corp. Amazon has challenged the award, in part claiming Mr. Trump had pressured the Defense Department to not give the company the contract, potentially worth $10 billion.

Amazon is now the third largest public company by value. Its stock is up around 33% this year, driven, in part, by booming sales, as consumers have flocked to the online retailer to stock up during the pandemic.

Mr. Musk's rise in the clubby world of the tech industry has run almost parallel to that of Mr. Bezos. Their rivalry is rooted in a space race currently playing out as a corporate version of the Cold War-era rivalry between the U.S. and the former Soviet Union. Mr. Musk, who also runs Space Exploration Technologies Corp., or SpaceX, has been critical of Mr. Bezos' own passion project, a rocket company separate from Amazon called Blue Origin.

SpaceX last week successfully sent U.S. astronauts into space in the first-ever private spacecraft to attain orbit with people on board. The mission was the culmination of years of work as part of the entrepreneur's broader dream of colonizing Mars.

Last year, Mr. Bezos took a not-so subtle swipe at Mr. Musk's Mars ambitions and his vision of the planet as a backup for life on Earth. "My friends who want to move to Mars?" Mr. Bezos said during a talk at the Wings Club, without naming Mr. Musk. "I say, do me a favor: Go live on the top of Mount Everest for a year first and see if you like it, because it's a garden paradise compared to Mars."

While Mr. Trump has been critical of the Amazon founder, he's shown increasing ties to Mr. Musk, especially as both men have pushed to reopen the U.S. economy.

Last month Mr. Musk won the president's support, as the CEO pressured local authorities in California to allow electric-car maker Tesla to resume production at his lone U.S. car plant. Manufacturing had been halted in March, as the Bay Area tried to combat the spread of the coronavirus. Mr. Musk fought a high-profile battle to restart production, eventually doing so in apparent violation of the local government's orders.

In an excerpt of his book, Mr. Berenson writes that the virus is more deadly than the seasonal flu in most years, though the fatality rate is far lower than last century's Spanish Flu pandemic.

He and Mr. Musk have engaged on Twitter in recent weeks. The Tesla CEO has repeatedly questioned the risk of Covid-19 and argued the threat of economic shutdown is greater, making him one of the highest profile business executives to question the government's response to the crisis.

After Amazon told Mr. Berenson his book was published, the author tweeted: "Of course I don't know what anyone who doesn't have @elonmusk and so many others pushing will do, but at least this time they backed down."

Jeffrey Trachtenberg contributed to this article.

Write to Tim Higgins at Tim.Higgins@WSJ.com