The comments, written in Pyongyang's official newspaper, follow criticism from Donald Trump in response to the death of American student Otto Warmbier, who was returned home in a coma after spending more than year in a North Korean prison.
Rodong Sinmun claimed Donald Trump was considering a pre-emptive strike on North Korea in order to divert attention from a political crisis in the US and said the president was in a "tough situation" at home.
"South Korea must realise that following psychopath Trump...will only lead to disaster," the newspaper wrote.
South Korean president Moon Jae-in is due to visit Washington next week to meet President Trump and told US media he wanted to begin talks with North Korea on its nuclear programme by the end of the year.
He called the leaders in Pyongyang an "irrational regime" in an interview with CBS television's This Morning.
Tensions between the US and North Korea have shown no signs of abating, with Mr Trump condemning the country for frequently flexing its military muscles.
The death of Mr Warmbier, who was jailed for 15 years with hard labour in 2016 for trying to steal a propaganda sign, prompted Mr Trump to condemn the "brutality of the North Korean regime".
"Otto's fate deepens my administration's determination to prevent such tragedies from befalling innocent people at the hands of regimes that do not respect the rule of law or basic human decency," he said.
A memorial service will be held for the 22-year-old student at Wyoming High School in Ohio on Thursday as the coroner continues to try to determine the cause of his death.