North Korea has accused Donald Trump of exploiting the death of American student Otto Warmbier, referring to the US president as an "old lunatic" for alleging the 22-year-old was tortured while in Pyongyang's custody.

In a statement issued by the state-run KCNA news agency, North Korea's foreign ministry accused the US of "luring and pushing" Warmbier, who died days after being released from North Korea in a coma, into breaking the country's laws. 

"Trump and his clique, for their anti-DPRK propaganda, are again exploiting the death of Otto Warmbier, an American college student who had been under reform through labor for the criminal act he committed against the DPRK and died after returning to the U.S," it said, using the acronym for the North's official name