But the speaking after the address, UK Foreign Secretary Johnson insisted military action was not the only option to deal with North Korea.
Northeast Asia analyst Marcus Noland, with the Peterson Institute for International Economics, wrote a blog post Tuesday saying from the North Korean perspective, Trump's speech reinforces the country's need for nuclear weapons to defend against and "existential threat by hostile foreign forces led by the United States".
The UN Security Council recently held two unanimous 15- to-0 votes adopting hard-hitting resolutions against North Korea, he said.
"And the bottom line is that, when the missiles - were they to be a threat, whether it be to USA territory, Guam, obviously Japan's territory - that would elicit a different response from us".
Mr Trump's most direct military threat to attack North Korea was his latest expression of concern about Pyongyang's repeated launching of ballistic missiles over Japan and underground nuclear tests.
However, none made any direct reference to Trump's belligerent message to the United Nations meeting.
North Korea has threatened the USA with a "horrible nuclear strike and miserable and final ruin", saying that it is ready to "destroy the enemies' bases" with a pre-emptive strike if they show "any slight sign of provocation".
"It is time for the entire world to join us in demanding that Iran's government end its pursuit of death and destruction", Trump said.
In its effort to punish Kim Jong Un for his continued defiance - repeated missile launches, a huge nuclear test - the United States has been leading a push to cut off oil to the isolated state.
He complimented Russian Federation and China for backing a unanimous Security Council resolution to place sanctions on North Korea, but called it an "outrage" that countries still trade with and provide financial assistance and arms to it.
The US President stunned the United Nations yesterday with a bellicose speech in which he threatened to "totally destroy" North Korea.
"If the righteous many don't confront the wicked few, then evil will triumph", Trump said.
Members of the administration have repeatedly emphasized that a range of military options are on the table and Mattis said Monday that the USA possess military options that would not put Seoul at risk of a North Korean counterattack with the potential to kill tens of thousands of civilians.
The US president used his speech to mock and threaten the North Korean leader.
North Korea's mission to the United Nations did not immediately respond to a request for comment on Trump's remarks.
In turning to Iran, Trump's criticism of the 2015 multilateral agreement to deter that country's nuclear weapons program echoed rhetoric he employed on the campaign trail.
He vowed again to take the fight to terrorists but warned that parts of the region were so plagued by violence and poverty, they were "going to hell".