JERSEY CITY — The biennial event is called the Presidents Cup, but until Sunday, the 13-year-old trophy had never been awarded to the winning team by a sitting President of the United States. The 45th president, Donald J. Trump, received a warm reception when he showed up at Liberty National Golf Course to hand the trophy to the United States squad after its 19-11 victory over the International team.

Long before he became a politician, Trump was an avid golfer and a golf course owner and developer. Until this year, one of his courses, in Doral, Fla., was the site of a World Golf Championships event. And the United States Women’s Open was held at one of his courses, Trump National Bedminster, an hour’s drive from Liberty National, in July.

He mingled easily with the players on both sides, many of whom he already knew — and a few of whom, like Ernie Els, the assistant captain of the International squad, he has played golf with since becoming president.

After Phil Mickelson closed out his 2 and 1 victory against Adam Hadwin in the final match on the course, Trump left his perch in the clubhouse and made his way to the 14th green for the trophy ceremony. As he came into view, some fans behind the hole broke into a rendition of “God Bless America.” Several others recited the Pledge of Allegiance.