Warning comes as Trump calls latest sanctions only a 'small step' and 'nothing compared' to what will have to be done.
North Korea has said the US will "suffer the greatest pain" over its role in the imposition of the latest sanctions on the country.
His comments come after the UN Security Council unanimously adopted a US-draft resolution slapping new sanctions on North Korea.
"The forthcoming measures … will make the US suffer the greatest pain it ever experienced in its history," Han Tae Song, North Korea's ambassador to the UN, said on Tuesday.
UN Security Council approves new sanctions on North Korea
The resolution is a water-down version of the original US proposal, but it does ban North Korea from importing all natural-gas liquids and condensates, as well as bans all textile exports and prohibits all countries from authorising new work permits for North Korean workers.
Han rejected the resolution as "illegal and unlawful" and said the US was "fired up for political, economic, and military confrontation".
North Korea is "ready to use a form of ultimate means", Han said.
On Wednesday, North Korea also called the sanctions a "heinous provocation aimed at depriving the DPRK of its legitimate right for self-defence and completely suffocating its state and people through full-scale economic blockade," according to a statement from the state-run Korean Central News Agency (KCNA).
DPRK stands for North Korea's formal name, the Democratic People's Republic of Korea.(Aljezira)