SEOUL, South Korea — President Moon Jae-in of South Korea proposed on Saturday that his country and North Korea form a unified team to compete in the 2018 Winter Olympics, to be held in the city of Pyeongchang in the South.

Mr. Moon made the overture during a speech at the opening ceremony of a World Taekwondo championship in the city of Muju in South Korea. The North does not compete in the championship but sent a demonstration team, led by Jang Woong, its delegate to the International Olympic Committee. It was the first sports exchange since Mr. Moon took office.

The South Korean president, who advocates dialogue and reconciliation with North Korea, recalled past instances where the two Koreas fielded joint teams in international sports competitions and their national teams marched together in Olympic Games.

“I want to see the same glory again,” he said, asking Mr. Jang for cooperation. “I want to feel the same Olympic sensation.”