Mr Kim had three high-profile summit meetings with Mr Trump and exchanged a series of letters, but the nuclear-armed state ended talks and said it would not engage further unless the US drops its hostile policies.
There was no immediate response from the White House and State Department, or South Korea’s government on Monday night.
South Korean and American troops began a joint springtime military drill last week, which was limited to computer simulations because of the coronavirus risk as well as the efforts to engage with the North.
“War drills and hostility can never go with dialogue and cooperation,” said Ms Kim, who has frequently attacked Seoul in state media dispatches.
She mocked South Korea for “resorting to shrunken war games, now that they find themselves in the quagmire of political, economic and epidemic crisis”.
The inter-Korean engagement that had improved in 2018 and is sought by South Korea “won’t come easily again” and North Korea will be watching to see if there is further provocations, she said.
North Korea would consider pulling out of a military agreement aimed at reducing tensions along their shared border, and would review whether to dissolve several organisations aimed at cooperation with the South, Ms Kim said.