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Trump: I have a 'much bigger' button than Kim Jong Un

President TrumpDonald John TrumpTrump to fundraise for 3 Republicans running for open seats: report Trump to nominate former Monsanto exec to top Interior position White House aides hadn’t heard of Trump's new tax cut: report MORE on Tuesday said that the nuclear launch button on his desk is "much bigger" and "more powerful" than that of North Korean leader Kim Jong Un – and that his button actually "works."

"North Korean Leader Kim Jong Un just stated that the 'Nuclear Button is on his desk at all times,'" Trump tweeted. "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!"

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Trump's comments came after Kim said in a New Year's Day speech that he had a nuclear launch button at his desk, and that the international community would have to accept North Korea's status as a nuclear-armed nation as a "reality."

In that address, Kim also said he was willing to send a delegation to the Winter Olympics in South Korea in February and engage in talks with Seoul about easing military tensions between the two countries.

South Korea responded to Kim’s remarks on Tuesday, calling for a dialogue between Seoul and Pyongyang aimed at de-escalating tensions ahead of the Winter Games.

Trump’s latest tweet, however, appeared to challenge Kim’s claim that North Korea has become a functional nuclear power, while delivering a warning that he stood ready to retaliate against a possible nuclear launch by Pyongyang.

The Trump administration has said little about the possibility of talks between North and South Korea, and Trump was unclear in a Tuesday morning tweet about whether the U.S. welcomed such a dialogue.

"Sanctions and 'other' pressures are beginning to have a big impact on North Korea," Trump tweeted. "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!"

- This story was updated at 8:24 P.M. EST.