Mr Kim also said his country would soon introduce “a new strategic weapon”.
But he left a door open for dialogue, and said the scope of any testing would depend on the US’s “attitude”.
The momentum of the past few years has stalled, as Washington refuses to lift sanctions until Pyongyang fully abandons its nuclear programme.
The North conducted several smaller weapons tests late in 2019, in what was seen as an attempt to pressure the US into making concessions.
But the self-declared moratorium on nuclear tests and tests of intercontinental ballistic missiles (ICBMs) that could reach the US mainland had been one of the foundations of the negotiations with Washington.
Pyongyang has not carried out such tests since 2017.