He also mocked Kim Jong-un with a disparaging nickname, saying: "Rocket man is on a suicide mission".
In his first address to the United Nations as US President, Trump said that the US was ready to "totally destroy" North Korea if it was forced to defend its allies, a warning seen as unprecedented for a US president delivering an address to the world's leaders and top diplomats.
North Korean leader Kim Jong-un responded to Trump's comments Thursday, calling the USA commander in chief's behavior "deranged".
"If the worldwide community wants to stop watching North Korea's provocations of nuclear weapons and missiles, they need to completely stop foreign money going into North Korea", he said in his native Korean language.
The ongoing war of words between the two leaders on opposite sides of the Pacific have been exacerbated in recent months amid growing tension over North Korea's nuclear weapons build-up.
North Korean Foreign Minister Ri Yong Ho's remarks before the United Nations General Assembly on Saturday came hours after US Air Force B-1B Lancer bombers escorted by fighter jets flew in global airspace over waters east of North Korea, in a show of force the Pentagon said demonstrated the range of military options available to Trump.
If North Korea follows through on its latest threat of setting off a nuclear explosion over the Pacific Ocean, it will ultimately be up to President Trump whether the United States will respond with military action, Secretary of State Rex Tillerson told ABC News today.
Tensions have escalated in the wake of North Korea's repeated missile launches and sixth nuclear test on September 3.
It could result in a further deteriorating relationship between North Korea and China, a benefactor of sorts to North Korea, and sabotage their economy.
The rhetorical combat continues as many other countries are concerned about potentially more serious consequences as North Korea quickens the pace of developing a nuclear-tipped intercontinental ballistic missile.
Trump also said China was imposing major banking sanctions, too, but there was no immediate confirmation from the North's most important trading partner.
It added that China has issued a "comprehensive ban on imported textiles" from North Korea.
The US and South Korea are technically still at war with North Korea because the 1950-53 war ended with a truce, not a peace treaty.
Numerous scientific agencies on both sides of the Pacific detected an quake Saturday near the site where North Korea set off a hydrogen bomb earlier this month, at first prompting speculation of another weapons test, before a consensus appeared to emerge that the tremor was a natural occurrence.