Mr. Parnas, who is facing federal charges in Manhattan, recently turned the documents over to the House Intelligence Committee as part of its impeachment inquiry.

One of the new documents shows Mr. Giuliani saying that he had Mr. Trump’s blessing to seek a meeting with Volodymyr Zelensky, Ukraine’s president-elect, last spring, potential new evidence on the eve of the president’s impeachment trial.

Mr. Giuliani has previously said he was acting at Mr. Trump’s direction in his dealings with Ukrainian officials, but the letter released on Tuesday is the first public document that says he was doing so.

“In my capacity as personal counsel to President Trump and with his knowledge and consent, I request a meeting with you on this upcoming Monday, May 13th or Tuesday, May 14th,” Mr. Giuliani wrote in the letter to Mr. Zelensky, who was sworn in as president soon after.

Mr. Giuliani shared a copy of the letter with Mr. Parnas, who then texted it to a close aide to Mr. Zelensky.