US President Donald Trump took to Twitter on Tuesday (2 January) to boast that his nuclear button is "much bigger" than that of North Korean leader Kim Jong-un's and Twitter is absolutely terrified.

"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!"

Trump's frightening and controversial remarks come after Kim said in a New Year's Day speech that the US should know he had a "nuclear button" at his desk.

After months of escalating tensions over North Korea's nuclear weapons program, Kim said the international community must accept the "reality" of the hermit kingdom as a nuclear-armed nation.

"The whole territory of the US is within the range of our nuclear strike and a nuclear button is always on the desk of my office and this is just a reality, not a threat," Kim said. The North Korean leader said he was "open to dialogue" with Seoul and the possibility of sending a delegation to the Winter Olympics in South Korea next month.

Twitter was left horrified by Trump's tweet that appeared to challenge Kim's claim with one person saying "nuclear war is not a game."

"Can somebody with intelligence approve these tweets before they are published into the real word. The real world. Real life, Donald. Not a f**king playground. Get a grip," one person wrote.

Many social media users have reported the president's alarming tweet for "threatening violence" and questioned Twitter why he hasn't been banned from the platform over the controversial post. The hashtag #JackIsComplicit taunting Twitter CEO Jack Dorsey has since gone viral.

"It's time. @Twitter , please suspend @realDonaldTrump . He literally just threatened the lives of millions of people using your social network," one person wrote.

Others have urged Congress to "stop this lunacy" and called for Trump to be impeached immediately.

Comedian Fortune Feimster wrote: "Donald Trump is pissing off a crazy man with nuclear weapons and people are on here still talking about how they don't like Hillary Clinton. What in the actual f**k?"

"Imagine being a servicemember or the family of a servicemember stationed in Korea and reading this," Democratic Senator Ed Markey wrote. "This borders on presidential malpractice."

Retired astronaut Mark Kelly said: "As a pilot in the @USNavy, I was trained to deliver nuclear weapons. EVERYTHING we did with these weapons was deadly serious. No jokes, no threats, no mistakes. Every soldier, sailor, airman and marine gets that."

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Twitter is terrified after Trump taunted Kim Jong-un saying his nuclear button is "bigger" and "more powerful" than the North Korean leader's REUTERS/Shannon Stapleton