Fresh from bipartisan criticism over comments equating Nazi and Klan followers with those who rallied against them in Charlottesville over the weekend, President Trump attacked Amazon.com Inc. (AMZN)  in a Tweet on Wednesday morning, claiming that the shopping website's growth has hurt U.S. retailers.

"Amazon is doing great damage to tax paying retailers. Towns, cities and states throughout the U.S. are being hurt—many jobs being lost!" Trump tweeted, shortly after 7 am EST.

The broadside against Amazon comes as The Washington Post, which is owned by Amazon founder Jeff Bezos separate from his company, has continued to report on Trump's comments about the violence in Charlottesville that led to the death of a 32-year-old woman, Heather Heyer, who was killed when a car allegedly driven by a white supremacist plowed into a crowd of demonstrators.

Trump has routinely portrayed The Post as peddling unfair coverage, or to use a favorite term of the president, "fake news," despite its reporting having been matched or followed by numerous other news organizations. In April, one of its reporters, David Fahrenthold, was awarded the Pulitzer Prize, the most prestigious award in journalism, for revealing that many of Trump's claims about his own philanthropy had been exaggerated over the years.

The early-morning offensive against Amazon raises the question of what the Trump administration might or could do to subvert one of the most successful U.S. companies in recent decades. Earlier this summer, Trump used Twitter to label Amazon a monopoly, suggesting that the online retailer be investigated for anti-competitive practices at odds with the Sherman Antitrust Act.

Amazon CEO Jeff Bezos.
Amazon CEO Jeff Bezos.

U.S. governments have used the Sherman Act to try to break up companies they alleged had used predatory practices to exploit monopolies.

In 1998, the federal government sued Microsoft Corp. (MSFT) , charging that the software maker had engaged in anti-competitive practices by bundling its Internet Explorer web browser with an operating system that had evolved into the industry standard on Intel-powered computers.

Yet unlike the government's case against Microsoft, Trump's attacks against Amazon are shrouded in the politics of red states versus blue states, and Bezos' ownership of The Washington Post. For more than a year, the Post has broken dozens of stories on the Trump campaign's ties to Russia, his firing of former FBI Director James Comey and his false claim that former President Barack Obama wiretapped him.

Trump, though, has struck back, insisting that the Post is being used by Bezos to protect Amazon from higher taxes, or even an antitrust investigation by the DOJ. While the matter of taxes was dealt with here, the issue of whether Amazon is exploiting a monopoly over certain markets is much harder to establish.

One thing is clear, Trump sees Amazon and The Post as a single entity, tied together by Bezos.

Watch: Sorry Gates, Buffett and Zuckerberg, Jeff Bezos Just Became the World's Richest Man

As he has done for months, the Republican president labeled the newspaper's work "fake news" despite wide acceptance of its veracity and supporting reports from numerous other news outlets.

Is Fake News Washington Post being used as a lobbyist weapon against Congress to keep Politicians from looking into Amazon no-tax monopoly?

— Donald J. Trump (@realDonaldTrump) July 25, 2017

So many stories about me in the @washingtonpost are Fake News. They are as bad as ratings challenged @CNN. Lobbyist for Amazon and taxes?

— Donald J. Trump (@realDonaldTrump) July 25, 2017

Leaving aside the political context of Trump's accusations, suing Amazon for antitrust violations would require meeting a difficult and daunting set of criteria, said Diana L. Moss, president of the American Antitrust Institute, a non-profit organization that promotes competition on behalf of consumers and businesses. The bar for proof in antitrust cases is much higher than in Europe, which succeeded in suing Alphabet's (GOOGL) Google, something the DOJ has yet to attempt. 

"It's a heavy lift," Moss said in a phone interview from Washington. "You have to prove that it's a monopoly, and that the monopolist has used its market power to extend or maintain that monopoly to the detriment of competition. There would have to be strong proof from market participants that Amazon engaged in exclusionary practices, and the government would have to be pretty concerned about its conduct in many of the markets that it participates in." 

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