North Korean leader Kim Jong Un enraged at Trump called the US President "mentally deranged US dotard".
Trump during his maiden address to the United Nations on Tuesday had said he would "totally destroy" North Korea and called Kim a "rocket man" on a suicide mission.
Japan described North Korea's threat to test a Hydrogen bomb as "totally unacceptable".
The Korean peninsula is on a knife's edge with North Korea testing missiles last week and threatening to destabilize the region with more tests.
The United States and South Korea jointly conducted military exercise in Pocheon in the north-eastern region of Gyeonggi province in South Korea as the Korean peninsula continued to simmer over Kim's military manoeuvres.