SEOUL—President Donald Trump deserves the Nobel Peace Prize for helping bring North Korea to the negotiating table, South Korea’s leader said, part of Seoul’s effort to credit the U.S. administration for spurring the recent thaw on the heavily militarized peninsula.

The remarks from South Korean President Moon Jae-in came three days after he met with North Korean leader Kim Jong Un at the inter-Korean demilitarized zone and agreed to push for a permanent peace treaty to formally end the Korean War.

“President Trump should win the Nobel Peace Prize,” Mr. Moon said Monday during a cabinet meeting, according to a spokesman for the presidential office in Seoul. “The only thing we need is peace.”

For the U.S., peace has meant that North Korea abandons its nuclear weapons. North Korea has said it would shut down its nuclear test site by May, though U.S. officials have expressed caution about the pledge.

The peace prize has already been awarded once for diplomacy with North Korea—in 2000, to South Korea’s then-president, Kim Dae-jung, who met with Kim Jong Un’s father, Kim Jong Il, in Pyongyang.