WASHINGTON — The White House signaled on Friday that it did not intend to mount a defense of President Trump or otherwise participate in the House impeachment proceedings, sending Democrats a sharply worded letter that condemned the process as “completely baseless” and urged them to get it over with quickly.

“House Democrats have wasted enough of America’s time with this charade,” the White House counsel, Pat A. Cipollone, wrote in a letter to the House Judiciary Committee chairman, Representative Jerrold Nadler of New York. “You should end this inquiry now and not waste even more time with additional hearings.”

The two-paragraph letter did not explicitly say what Mr. Trump’s legal team planned to do, but it ended by quoting the president saying that the House should hold a swift vote on impeachment to speed the way for a trial in the Republican-controlled Senate, where White House officials believe Mr. Trump will have a better chance to mount a defense. People close to the White House said that it would take major concessions by Democrats for that position to change.