SEOUL, South Korea — Several months ago, South Koreans considered President Trump as dangerous as North Korea’s leader, Kim Jong-un, as the two traded threats of nuclear annihilation.

Now, commentators and others in Seoul think Mr. Trump deserves a Nobel Prize for helping start the unexpected peace process unfolding on the divided Korean Peninsula. On Monday, South Korea’s president, Moon Jae-in, said he felt the same.

Mr. Moon’s endorsement of a Nobel for Mr. Trump, who has faced one ethical scandal after another at home, came as the South Korean leader presided over a meeting of his senior presidential staff on Monday. During the meeting, Mr. Moon received a telegram from Lee Hee-ho, a former first lady of South Korea, congratulating him for a successful summit meeting with Mr. Kim on Friday and wishing him a Nobel Peace Prize.

“It’s really President Trump who should receive it; we can just take peace,” Mr. Moon was quoted by his office as saying.