President Trump in a tweet Tuesday evening mocked the leader of North Korea, saying his own "nuclear button" works and is "bigger and more powerful" than Kim Jong Un's.

"Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!," Trump tweeted.

The tweet comes a day after Kim gave his customary yearly address to his country, announcing North Korea had achieved the historic feat of "completing" its nuclear forces and adding he has a nuclear button on his desk.

"The U.S. should know that the button for nuclear weapons is on my table," he said during the speech, as translated by The Associated Press.

"The entire area of the U.S. mainland is within our nuclear strike range. ... The United States can never start a war against me and our country," Kim said.

Kim Jong Un also said Monday the United States should be aware that his country's nuclear forces are now a reality, not a threat. But he also struck a conciliatory tone in his New Year's address, wishing success for the Winter Olympics set to begin in the South in February and suggesting the North may send a delegation to participate.

The Associated Press contributed to this report.