WASHINGTON — As Donald J. Trump was preparing to deliver an address on energy policy in May 2016, Paul Manafort, his campaign chairman, had a question about the speech’s contents for Thomas J. Barrack Jr., a top campaign fund-raiser and close friend of Mr. Trump.

“Are you running this by our friends?” Mr. Manafort asked in a previously undisclosed email to Mr. Barrack, whose real estate and investment firm does extensive business in the Middle East.

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Mr. Barrack was, in fact, coordinating the language in a draft of the speech with Persian Gulf contacts including Rashid al-Malik, an Emirati businessman who is close to the rulers of the United Arab Emirates.

The exchanges about Mr. Trump’s energy speech are among a series of interactions that have come under scrutiny by federal prosecutors looking at foreign influence over his campaign, his transition and the early stages of his administration, according to documents and interviews with people familiar with the case.