WASHINGTON—President Trump praised the performance of his Supreme Court nominee, joked about a supporter’s divorce and claimed the upper hand in the trade negotiations with Canada during an 80-minute, campaign-style speech he delivered Thursday night at a private fundraiser, according to people who attended the event.

Described by attendees as energized and enthusiastic, the president arrived late to the party inside a ballroom at his Washington hotel, then delivered a lengthy speech in front of 300 people, including about...