WASHINGTON — President Trump on Monday awarded Tiger Woods the Presidential Medal of Freedom, the nation’s highest civilian honor, in a Rose Garden ceremony in which both men described the golfer’s athletic triumphs set against painful personal lows.

“I’ve battled,” Woods, 43, said after the president fastened the medal around his neck. “I’ve tried to hang in there, and I’ve tried to come back and play the great game of golf again.”

The fight Mr. Woods described was what Mr. Trump seemed to admire most. He cited the golfer’s “relentless will to win, win, win,” in a speech that traced in detail Mr. Woods’s career from his being named the PGA Tour’s rookie of the year in 1996 to his against-the-odds comeback with last month’s win at the Masters.

“We can’t wait to see what’s next, Tiger,” Mr. Trump said to Mr. Woods, a normally sedate figure who spent Monday’s ceremony grinning ear to ear. “There are no winners like you.”