In a tense meeting in early March with the special counsel, President Trump’s lawyers insisted he had no obligation to talk with federal investigators probing Russia’s interference in the 2016 presidential campaign.

But special counsel Robert S. Mueller III responded that he had another option if Trump declined: He could issue a subpoena for the president to appear before a grand jury, according to four people familiar with the encounter.

Mueller’s warning — the first time he is known to have mentioned a possible subpoena to Trump’s legal team — spurred a sharp retort from John Dowd, then the president’s lead lawyer.

“This isn’t some game,” Dowd said, according to two people with knowledge of his comments. “You are screwing with the work of the president of the United States.”