South Korea's President Moon Jae-In said the North was inching "closer to the threshold of the red line."
By the time the war ended, nearly 1.8 million Americans fought in the conflict, nearly 37,000 soldiers died and more than 7,800 remain unaccounted for to this day.
The two men met at the Asian Leaders Conference in the South Korean capital.
North Korea's leader may be as secretive as his father and grandfather, but we know a little about how he spends his days.
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.