SEOUL — President Trump has the unwavering support of South Korea’s leftist Democratic, or Minju, party in his quest for the Nobel Peace Prize.

Mr. Trump, while meeting with Prime Minister Netanyahu at the White House, assessed the odds of his winning the prize, remarking, “I deserve the Nobel, but they will never give it to me.” Later, though, a member of Korea’s national assembly, Park Sun-won, disclosed that he had nominated the president for the prize for his “efforts toward North Korea’s denuclearization and his contributions to peace on the Korean peninsula.”