Trump also mocked North Korean leader Kim Jong Un in the speech, dubbing him "Rocket Man".
North Korean Foreign Minister Ri Yong Ho also said on Thursday that Kim was considering testing "an unprecedented scale hydrogen bomb" over the Pacific in response Trump's United Nations speech. After North Korea threatened to launch a missile at the American territory Guam, Mr Trump promised that the USA would bring "fire and fury" to North Korea if the country continued to threaten the United States and its allies.
The North Korean also said that Trump comments were reflective of "mentally deranged behaviour".
An executive order allowing Washington to ramp up fresh sanctions against North Korea has been signed by US President, Donald Trump, with the latest measure banning foreign banks and businesses doing any trade with Pyongyang.
The dispatch was unusual in that it was written in the first person, albeit filtered through the North's state media, which are part of propaganda efforts meant to glorify Kim.More news: No long queues in Hong Kong on iPhone 8 launch day
MCEVERS: And he demeaned Trump's rhetoric, saying he was, quote, "surely a rogue and a gangster fond of playing with fire rather than a politician".
North Korean leader Kim Jong Un guides a target-striking contest of the special operation forces of the Korean People's Army (KPA) to occupy islands in this undated picture provided by KCNA in Pyongyang on August 25, 2017.
North Korea's six previous nuclear tests have all been conducted underground.
Nuclear proliferation watchdog CTBTO said on Saturday it had detected two seismic events in North Korea on Saturday but they were probably not deliberate explosions in the isolated country.
"If (China) follows through on what they did that could be a game changer", said Cashin, UBS director of floor operations at the New York Stock Exchange.
China, North Korea's ally and arbiter of stability in the region, called on all parties to exercise restraint after the incendiary remarks.
A hydrogen bomb test has not been conducted in decades and would be wrought with peril.