WASHINGTON—President Trump on Tuesday sought to extinguish questions about the future of U.S. relations with Saudi Arabia, pledging to remain a “steadfast partner” of the kingdom and dismissing U.S. intelligence conclusions that the Saudi crown prince had ordered the killing of a dissident journalist last month.

In a White House statement that the president appeared to have penned himself, Mr. Trump suggested the U.S. wouldn’t impose further punishment on Saudi Arabia over the killing and said it was unknowable whether Crown...