Some of the president’s closest advisers were involved in drafting the letter, but they did not include Pat A. Cipollone, the White House counsel who will play a large role in a Senate trial.

Instead, Eric Ueland, the director of the Office of Legislative Affairs, led the process, with input from Stephen Miller, the president’s top policy adviser, who often scripts many of Mr. Trump’s public remarks. Michael Williams, an adviser to Mick Mulvaney, the president’s acting chief of staff, also weighed in, and Mr. Ueland’s draft was framed over the last few days.

Former presidential advisers said documents like these were always a reflection of the person in charge. To them it seemed clear that, on the eve of impeachment, Mr. Trump was interested in speaking only to his base.

“There just doesn’t seem to be a lot of strategy,” said David Litt, a former speechwriter for President Barack Obama. “Nothing here suggests that he’s trying to talk to someone who is trying to make up his or her mind” on impeachment.