United Nations: In his maiden address to the UN General Assembly, US President Donald Trump on Tuesday trumpeted his own achievements and pledged to "totally destroy" North Korea after calling its regime a "band of criminals".

Amid escalating crisis in the Korean peninsula, a combative Trump referred to "rogue nations" as "the scourge of our planet." Moments later, he called out North Korea by name, rattling off a list of human rights violations in that country.

Speaking about North Korea's nuclear threat, he dubbed the Pyongyang regime "depraved" and a "band of criminals". He urged the UN to further isolate it by imposing more sanctions and threatened to "totally destroy" the country.

He referred to North Korean leader Kim Jong-un a "rocket man", adding that the dictator was on a suicide mission with his nuclear programme that has triggered global concerns.

Trump, who took office in January, also focused on himself.

He opened his address by saying that the US had done well since he entered the White House. The stock market was at an all time high and unemployment in the US was at its lowest level.

Trump told the world leaders at the UN that terrorists were gaining strength everywhere but insisted that peace was possible.

"To put it simply, we meet at a time of both immense promise and great peril. Terrorists and extremists have gathered strength and spread to every region of the planet."

The US, he said, was prepared to combat global instability through military might. "Our military will soon be the strongest it has ever been."

He underlined that he would always put American interests above all else. And he quickly urged other nations to do the same.

"In America, we do not seek to impose our way of life on anyone, but rather to let it shine as an example for everyone to watch."

Over the past week, Trump has signalled his frustrations with the Iranian nuclear deal that former President Barack Obama made.

On Tuesday, he derided the deal. "Frankly, that deal is an embarrassment to the United States, and I don't think you've heard the last of it - believe me."

His comments came a day after Iranian President Hassan Rouhani warned that the US would pay a "high cost" if Trump scrapped the agreement.