Instead, he has continued making money, as he has for decades, working with the same Persian Gulf contacts he introduced two years ago to Mr. Trump. Mr. Barrack’s company, known as Colony NorthStar since a merger last year, has raised more than $7 billion in investments since Mr. Trump won the nomination, and 24 percent of that money has come from the Persian Gulf — all from either the U.A.E. or Saudi Arabia, according to an executive familiar with the figures. Colony NorthStar has not disclosed the investors in its funds.

Mr. Barrack’s email correspondence with Ambassador Otaiba, which has not previously been reported, was provided to The New York Times by an anonymous group critical of Emirati foreign policy, and it illustrates the formative role Mr. Barrack played as a matchmaker between Mr. Trump and the Persian Gulf princes.

Mr. Barrack’s representatives did not dispute the authenticity of the emails. His spokesman said in a statement that Mr. Barrack “sees his business in the Middle East as a way to help political dialogue and understanding, not the other way around, and he does so through relationships that span as far back as the reign of even some of the grandfathers of the current regional rulers.”

But having the ear of the president, say other executives and former diplomats who work in the gulf, has only enhanced Mr. Barrack’s stature in the region.

“He is the only person I know who the president speaks to as a peer,” said Roger Stone, a veteran Republican operative who has known both men for decades. “Barrack is to Trump as Bebe Rebozo was to Nixon, which is the best friend,” Mr. Stone added, referring to the wealthy real-estate developer who is best remembered for his closeness to President Richard Nixon during his impeachment process.

Mr. Barrack’s closeness to Mr. Trump extends to the president’s family. By 2010, he had acquired $70 million of the debt owed by Mr. Trump’s son-in-law, Jared Kushner, on his troubled $1.8 billion purchase of a skyscraper at 666 Fifth Avenue in New York. After a call from Mr. Trump, Mr. Barrack was among a group of lenders who agreed to reduce Mr. Kushner’s obligations to keep him out of bankruptcy.

A month after his first outreach to Ambassador Otaiba, Mr. Barrack wrote again on May 26 to introduce Mr. Kushner, who was preparing for a role as a presidential envoy to the Middle East.