Ahead of talks here next week with President Donald Trump, Moon said he hopes to engage North Korea in dialogue by the end of the year.
But Moon also said that as North Korea pursues its nuclear weapons program, he can envision a worsened scenario in which he and Trump might some day start talking about launching a pre-emptive strike against the Pyongyang regime.
"I believe that we will probably have such discussions," Moon said.
He had been sentenced for stealing a political poster from his hotel.
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Warmbier was medically evacuated to the United States a week ago, suffering from severe brain damage. He died six days later surrounded by relatives in his hometown of Cincinnati.
"Yes, this had happened while Mr Warmbier was in the detention of North Korean authorities," Moon told CBS television's "This Morning."
"We cannot know for sure that North Korea killed Mr Warmbier, but I believe it is quite clear that they have a heavy responsibility in the process that led to his death," the president added.
Medical tests in the United States offered no conclusive evidence as to the cause of his neurological injuries, and no evidence of a prior botulism infection.
Asked how the Warmbier case would affect Moon's efforts to engage North Korea as he has said he wants to, the president added: "I believe we must now have the perception that North Korea is an irrational regime.
"Working with such a country, we must achieve the goal of the complete dismantlement of North Korea's nuclear program," Moon said.
Trump too has signaled a willingness to try a different tack with North Korean leader Kim.
Still, Defense Secretary James Mattis said this month that "the regime's nuclear weapons program is a clear and present danger to all" and Pyongyang continues to behave provocatively despite UN censure and sanctions.
Despite the possibility of a ramped up conflict, Moon said dialogue with the North is necessary, though he will not rush into it, and hopes it can take place by the end of the year.