The magazine — which refers to Saudi Arabia throughout as “the Magic Kingdom” — includes an interview with Mr. Grine, accompanied by a photo of him posing with Mr. Trump in the Oval Office, taken during his visit with Mr. Pecker. It talks up the relationship between Mr. Trump and the Saudis, noting that Mr. Trump “endorsed the crown prince’s high profile anticorruption” crackdown.

A.M.I. has said it produced the magazine to “capitalize” on interest in the crown prince, who is next in line to the throne, and has been careful to say it received no input or guidance from Saudi officials. That carries important legal implications: Foreign direction or control of such a purely promotional publication may require disclosure to the Justice Department. The Saudi government did not respond to a request for comment.

The magazine — 200,000 copies distributed in Walmart and other outlets, with a cover price of $13.99 and no advertising — provided a unique welcome mat for the prince, whose visit comes as the Trump administration is trying to establish tighter ties with the kingdom. Both countries are touting cross-border investment opportunities, including a pledge by the Saudi government to put $20 billion into a fund that will invest in American infrastructure projects. The kingdom is also nearing a deal to buy American-made missiles and other military equipment.

Mr. Grine, a 30-year-old French citizen, has helped broker deals between Saudi investors and companies in France, Senegal and the United States. He and Mr. Pecker were introduced last spring by Ari Emanuel, chief executive of Endeavor, the huge talent, entertainment and sports company based in Beverly Hills, Calif.

Image Mr. Trump with Karen McDougal, a former Playboy model who claims they had an affair. Mr. Pecker’s company suppressed the story during the presidential campaign.

Mr. Grine and Mr. Pecker soon had a series of discussions about the investment landscape in Saudi Arabia, according to a person briefed on the talks. Mr. Pecker extended the White House dinner invitation shortly afterward.

A.M.I. would not say who else was among the “select group of friends” Mr. Pecker took to the White House at the president’s invitation. During the evening, the Middle East and the recent French elections came up. In a statement, A.M.I. said, “The entire conversation was social, with the exception of a couple very brief mentions of current events.”