North Korea said last month that it was its sovereign right to "ruthlessly punish" U.S. citizens it had detained for crimes against the state.
"I believe we must now have the perception that North Korea is an irrational regime", said Moon, who was elected in May.
It comes as South Korean President Moon Jae-in says North Korea should swiftly return South Koreans and Americans detained in the reclusive nation and that Pyongyang has "a heavy responsibility" in the death of Warmbier. "At least I know China tried!"
The question of what exactly happened to Otto Warmbier in North Korea will, sadly, probably never be answered. They did not cite a specific cause of death. Three other Americans are still being held captive there.
If Washington imposes sanctions on Chinese enterprises, it would lead to "grave friction" between the two countries, said the paper, which does not represent Chinese government policy.
A small aircraft, which South Korea's Military says is a drone from North Korea, is seen at the Defense Ministry in Seoul, South Korea, June 21, 2017.
"If the administration is smart, they'll use this as one more reason why sanctions, isolation and coercion need to be the tip of the spear against North Korea", said Medeiros, now an analyst at the Eurasia Group.
Doctors at the Cincinnati Medical Center, where Mr Warmbier was treated following his return to the U.S. on 13 June, determined he suffered from "unresponsive wakefulness", also known as persistent vegetative state, due to "severe neurological injury".
Dennis Rodman, NBA legend and pop culture enigma, has come under a lot of fire as of late due to both praising and defending North Korean dictator Kim Jong-un. President Moon strongly condemned the North, saying the rogue state bears "heavy responsibility" for the 22-year-old's death and urged Pyongyang to release the other South Korean and US citizens held there, vowing to make all-out efforts for their release. But on Tuesday, Trump suggested that strategy had failed.
White House press secretary Sean Spicer said the administration would "continue to apply economic and political pressure" on North Korea, in conjunction with USA allies and China, "to change this behaviour and this regime".
"We can launch and operate long-range bombers over the Korean peninsula on very short notice, and we hope not to have to do that", Pentagon spokesman US Navy Capt. Jeff Davis said.
Warmbier died in OH on Monday, days after being released by North Korea while in a coma. On the day before Trump picked up his smartphone, United States press secretary Sean Spicer announced that the White House believed that China had made "positive movement" towards dispelling North Korea's anti-American antics.
In an interview in the spring, Trump said he would be "honored" to meet with Kim under the right circumstances, and he proclaimed that the United States was prepared to handle the threat from Pyongyang on its own if China was unable to do so.
Washington has some 28,000 troops deployed in South Korea and a naval armada in the region.
The Trump administration doesn't need an act of Congress to bar Americans from traveling to North Korea.
The US side is expected to press China to cooperate on a further toughening of global sanctions on North Korea.