By Tim Higgins

Elon Musk on Thursday took aim at Amazon.com Inc. and its founder Jeff Bezos, calling for a breakup of the online retail giant after it had rejected a book questioning the risk of the coronavirus pandemic, a topic the Tesla Inc. chief executive has expressed strong views on.

"Time to break up Amazon. Monopolies are wrong!" Mr. Musk said on Twitter in response to a tweet by Alex Berenson, an author who said that Kindle Direct Publishing, Amazon's outlet for self-published e-books, had rejected his submission for a Covid-19-related book. Mr. Musk initially responded: "This is insane @JeffBezos."

The book was removed in error and was being reinstated, an Amazon spokeswoman said. She didn't address Mr. Musk's claim that the company was a monopoly that should be broken up

Soon after Mr. Musk's message, the author 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."

The book that sparked Mr. Musk's criticisms of Mr. Bezos on Thursday is called "Unreported Truths about Covid-19 and Lockdowns: Part 1: Introduction and Death Counts and Estimates."

In an excerpt of the book posted online, 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 as 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 businessmen to question the government's response to the crisis.

Mr. Musk and Mr. Bezos have a history of taking jabs at each other, rooted in a space race that is playing out between the two billionaires, a corporate version of the Cold War-era rivalry between the U.S. and the former Soviet Union to dominate space. 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 long-held ambition of going to Mars, which Mr. Musk has said humans should do 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."

Amazon has come under political pressure for some of its business practices from politicians in both parties. Former Democratic presidential candidates Sen. Elizabeth Warren of Massachusetts and Vermont's Sen. Bernie Sanders each called for Amazon to be broken up due 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 data on third-party sellers on its platform to develop its products.

President 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 Dept not to give it the contract potentially worth $10 billion.

Mr. Musk last month won backing from Mr. Trump as he pressured local authorities in California to allow electric-car maker Tesla to resume production at his lone U.S. car plant after manufacturing was halted in March as the Bay Area tried to combat the spread of the coronavirus. Mr. Musk filed a lawsuit in an attempt to restart production before doing so in apparent violation of the local government's orders.

The rivalry between Mr. Musk and Mr. Bezos took a new twist last month with Amazon exploring the possible acquisition of a driverless-car technology startup called Zoox Inc. Amazon has investments in electric-car startup Rivian Automotive LLC and self-driving car startup Aurora Innovation Inc., which was co-founded by a former Tesla executive who helped develop Mr. Musk's technology.

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