Trump was responding to Kim's annual New Year's Day speech on Monday, during which the North Korean leader boasted that the United States is "within the range of our nuclear strike and a nuclear button is always on the desk of my office."
Trump said in his Tuesday tweet, "North Korean Leader Kim Jong Un just stated that the 'Nuclear Button is on his desk at all times.' 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!"
The exchange represents a ratcheting up of rhetoric, after Trump in recent months had adopted a measured approach to North Korea — relative to last summer, when he warned of "fire and fury" — at the urging of his national security team.
Earlier Tuesday, however, Trump revived his derisive nickname for Kim — "rocket man" — in response to signs of relaxed tensions between South Korea and North Korea. South Korea agreed to an offer from North Korea for the two countries to talk ahead of next month's Winter Olympic Games in PyeongChang, South Korea. Kim said in his Monday address that he was willing to send a delegation of North Korean athletes to the Olympics.
In his Tuesday tweet, Trump wrote: "Sanctions and 'other' pressures are beginning to have a big impact on North Korea. Soldiers are dangerously fleeing to South Korea. Rocket man now wants to talk to South Korea for first time. Perhaps that is good news, perhaps not — we will see!"
Trump's North Korea comments came on a busy day of tweeting for the president, who called for the Justice Department to prosecute and perhaps jail Hillary Clinton adviser Huma Abedin and former FBI director James B. Comey; threatened to strip funding for the Palestinians; encouraged protesters in Iran; took credit for the safety record of commercial airlines; and attacked the news media.