South Korea has fast-tracked the plan after a series of missile tests by Pyongyang.
“I believe it is quite clear that they have a heavy responsibility in the process that led to Mr. Warmbier's death,” Moon Jae-in said.
Despite the South Korean president's attempts to open dialogue, the North has made several moves that raise tensions.
A suspected North Korean drone was found with photos of THAAD by South Korean military officials after it crashed near the nations' mutual border.
“Mom did everything and I didn’t know anything,” Chung Yoo-ra, 20, said in January.
"We want it to be the peace Games," the organizing committee chief said.
The warning from South Korea's new president comes despite his more diplomatic tone toward North Korea.
Sunday's test was detected by the U.S.-developed THAAD anti-missile system, despite much controversy surrounding its installation last month.
Moon Jae-in has set out his plan to ease tensions on the Korean peninsula.
The two leaders agreed to work toward peace on the Korean peninsula.
The election of Moon Jae-in, a dovish leader in South Korea, could complicate Donald Trump’s plans to stop North Korea’s nuclear weapons programs.
According to polls, liberal Moon Jae-in is likely to sweep to victory.
South Korea's probable new president is set to shake up the status quo in relations with North Korea and the United States.
North Korea's state-run media outlet called on South Koreans to 'wage unflinching struggle' against the U.S.'s missile defense system.