In the Middle East, Mr. Greenblatt’s tweets have done little to repair the rift with the Palestinians or lay the groundwork for his long-anticipated peace plan. In a recent exchange, Mr. Greenblatt accused the longtime Palestinian negotiator, Saeb Erekat, of unfairly maligning the proposal when he warned that it would be “an apartheid system with ghettos for Palestinians.”

Mr. Grenell, whose no-holds-barred style most closely mirrors Mr. Trump’s, infuriated his German hosts last May when he tweeted, after the president’s decision to abandon the Iran nuclear deal, that “German companies doing business in Iran should wind down operations immediately.” Germany had opted to stay in the deal.

All of the president’s advisers pay close attention to his social media behavior and copy some of his moves. Mr. Bolton, for example, has taken his lead in pounding a message through sheer repetition: Mr. Bolton’s 150-plus tweets on Venezuela are not unlike Mr. Trump’s repeated references to the special counsel’s Russia investigation as a “witch hunt.”

Mr. Bolton told CNN that the tweets were a “new experiment in public diplomacy” — never mind that Mr. McFaul, and later Secretary of State John Kerry, did it during the Obama administration.

A longtime commentator on Fox with a penchant for pungent statements, Mr. Bolton sometimes infuses his tweets with a distinctly Trumpian tone. “Talks between Russia and Maduro’s cronies are only useful if they are discussing retirement beaches for Maduro,” he wrote last week of Russian efforts to broker a solution to the crisis.

The difference between Mr. Trump and his advisers is that his tweeting is usually more ad hoc. He has been known to tap out his messages off the cuff and not have them vetted, with a “watch this” expression, according to two people who have seen him do it.