Mr. Bezos did not respond to a request for comment.

The Washington Post declined to make Mr. Baron available for an interview but the paper did provide a statement from him.

“Jeff has never gotten involved in our reporting or our final stories,” he said. “People surmise that it must be difficult to cover Jeff and Amazon. But we’ve gone five and a half years with his ownership, and he hasn’t once intervened in any way.”

The clash between Mr. Bezos and The Enquirer began last month when the tabloid published an exposé of his extramarital affair with the television personality Lauren Sanchez. Mr. Bezos fought back in his remarkably revealing blog post on Medium, the online open platform. He accused David J. Pecker, the chairman of The Enquirer’s parent company, American Media Inc., of threatening through intermediaries to publish graphic photographs of Mr. Bezos if he did not publicly announce that The Enquirer’s reporting on his affair was not politically motivated.

The Post has traditionally focused on the nation’s capital, with not as many resources devoted to business coverage. That has started to change. The Post had previously said it would nearly double the number of journalists devoted to covering Silicon Valley to 25, including a reporter in Seattle who will focus on Amazon.

It also aggressively followed up on the revelation about Mr. Bezos’ private life.

The Post published a lengthy article on Feb. 5 about The Enquirer’s coverage of Mr. Bezos’ affair. It quoted Gavin de Becker, his longtime security chief, as saying the leak of evidence of Mr. Bezos’ infidelity to The Enquirer was “politically motivated,” designed to embarrass Mr. Bezos because he owns The Post. Mr. de Becker added that the effort could also involve figures from President Trump’s campaign.

Emails from American Media that Mr. Bezos included in his blog post referred to the Post article and demanded that he — and the newspaper — refrain from any statements or suggestions that politics played any part in its coverage of his affair with Ms. Sanchez.

Like other newspapers, including The New York Times, The Post ran front-page articles on Mr. Bezos and American Media on Friday and Saturday. Those were not the only articles about his interests. The paper also published a report about Amazon’s potentially pulling out of its agreement to build a headquarters in New York City, as well as one about a lawsuit filed against Amazon by the director Woody Allen, who said its streaming service had improperly backed out of a four-movie deal with him.