Donald Trump has boasted that he has a bigger and more powerful “nuclear button” than North Korean leader Kim Jong Un — but the US president does not actually have a physical button.

The president’s tweet came in response to Mr Kim’s new year address in which he repeated fiery nuclear threats against the US.

Mr Kim said he has a “nuclear button” on his office desk and warned that “the whole territory of the US is within the range of our nuclear strike”.

Mr Trump replied: “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!”

Despite ratcheting up the tension, Mr Trump does not have a nuclear button.

The process for launching a nuclear strike is secret and complex and involves the use of a nuclear “football”, which is carried by a rotating group of military officers everywhere the president goes and is equipped with communication tools and a book with prepared war plans.

If the president were to order a strike, he would identify himself to military officials at the Pentagon with codes unique to him.

The codes are recorded on a card known as the “biscuit” which is carried by the president at all times.

He would then transmit the launch order to the Pentagon and Strategic Command.

Earlier on Tuesday, Mr Trump sounded open to the possibility of an inter-Korean dialogue after Mr Kim made a rare overture towards South Korea in his new year address.

But Mr Trump’s ambassador to the United Nations insisted talks would not be meaningful unless the North was getting rid of its nuclear weapons.

In a morning tweet, Mr Trump said the US-led campaign of sanctions and other pressure were beginning to have a “big impact” on North Korea.

He referred to the recent, dramatic escape of at least two North Korean soldiers across the heavily militarised border into South Korea.

He also alluded to Mr Kim’s comments on Monday that he was willing to send a delegation to the Winter Olympics, which will be hosted by South Korea next month.

“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!” Mr Trump said, using his derisive nickname for the young North Korean leader.