His comments rattled the world leaders gathered before him in the green-marbled UN General Assembly hall, where minutes earlier UN Secretary-General Antonio Guterres had appealed for statesmanship.
“The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea,” Trump said.
"The United States is ready, willing and able. But hopefully, this will not be necessary. That's what the United Nations is all about. That's what the United Nations is for. Let's see how they do.
"It is time for North Korea to realise that the denuclearisation is its only acceptable future," he asserted.
The UN Security Council recently held two unanimous 15- to-0 votes adopting hard-hitting resolutions against North Korea, he said.
He thanked China and Russia for joining the vote to impose sanctions, along with all the other members of the Security Council.
"Thank you to all involved," he said.
"But we must do much more. It is time for all nations to work together to isolate the Kim regime until it ceases its hostile behaviour," he added.
In a thunderous 41-minute speech, Trump also took aim at Iran’s nuclear ambitions and regional influence, Venezuela’s collapsing democracy and the threat of Islamist extremists.
"We face this decision not only in North Korea. It is far past time for the nations of the world to confront another reckless regime, one that speaks openly of mass murder, vowing death to America, destruction of Israel and ruin for many leaders and nations in this room," he added, pointing to Iran.
Trump said North Korea's reckless pursuit of nuclear weapons and ballistic missiles threatens the entire world with the unthinkable loss of human life.
"It is an outrage that some nations would not only trade with such a regime, but would arm, supply and financially support a country that imperils the world with nuclear conflict," he said.
As loud, startled murmurs filled the hall, Trump described Kim in an acid tone, saying, “Rocket Man is on a suicide mission for himself and his regime.”
One man in the audience covered his face with his hands shortly after Trump made his “totally destroy” comment. Swedish Foreign Minister Margot Wallstrom crossed her arms.
North Korea’s mission to the United Nations did not immediately respond to a request for comment on Trump’s remarks. A junior North Korean diplomat sat in the delegation’s front-row seat for Trump’s speech, the North Korean UN mission said.
Trump’s saber-rattling rhetoric was in contrast to the comments of some of his own Cabinet members who have stated their preference for a diplomatic solution.
He also criticised the Cuban government.
“Major portions of the world are in conflict and some, in fact, are going to hell,” he said.
In what may have been a veiled prod at China, the North’s major trading partner, Trump said: “It is an outrage that some nations would not only trade with such a regime but would arm, supply and financially support a country that imperils the world with nuclear conflict.”
Turning to Iran, Trump called the 2015 nuclear deal negotiated by his predecessor, Barack Obama, an embarrassment and hinted that he may not recertify the agreement when it comes up for a mid-October deadline.