The US President described Pyongyang's leader Kim Jong Un as a "rocket man on a suicide mission for himself and his regime" in his sternest warning yet to North Korea.
A senior administration official said the president will deliver a message that "nations can not be bystanders in history - and that if we don't confront the threat now they will only gather force and become more formidable as time passes".
While the US could take military action itself, Trump urged the United Nations to join together in curtailing North Korea's nuclear efforts.
In recent weeks, critics of the accord have also seized on North Korea's provocations and long-term pursuit of nuclear weapons as proof the US needs to get tougher on Iran to prevent a similar threat.
Trump also said it is "far past time" for the nations of the world to confront Iran, which he called a "reckless" and "murderous regime" that is "undermining peace throughout the Middle East".
In an indictment of the global body, Mr. Trump said the Iran nuclear deal provides a "cover for the potential construction of a nuclear program" in the region, an outcome that the USA would not tolerate.
Speaking at the UN General Assembly in NY for the first time, Mr Trump said: "The United States is ready, willing and able (to act), but hopefully this will not be necessary".
But the president stood before world leaders and a global audience and declared that U.N. members, acting as a collection of self-interested nations, should unite to confront global dangers.
Directly putting the country's leader on notice, Trump suggested Kim Jong Un could not survive an American attack.
"Maduro has defied his own people, stealing power from their elected representatives to preserve his disastrous rule", Trump said.
That was thoroughly absent from this address, which clearly bore the stamp of Stephen Miller, Trump's bellicose policy adviser, who surely must have been the last to be picked for sports teams when he was a youth.
The appeal encourages individual member states to adopt a line similar to Trump's nationalistic "America First" campaign slogan. "Just like you, the leaders of your countries, should and always put your countries first", Trump said to applause.
Many world leaders, concerned about America's priorities and role in the world, will get their first chance to hear and meet Trump.
Trump also singled out Iran, calling the Iran nuclear deal, which was brokered by former President Barack Obama, an "embarrassment" for the US.
"The United States has great strength and patience". "But in fulfilling our obligations to our own nations, we also realize that it's in everyone's interest to seek a future where all nations can be sovereign, prosperous and secure".
But while China is responsible for the overwhelming majority of trade with North Korea, Trump's lack of direct criticism of the two countries gave insight into the President's approach to the US' disagreements and often adversarial relationships with the two countries - particularly at a time when he needs the two countries to support U.S. efforts to ramp up pressure on North Korea.
He thundered often about putting "America first", and has withdrawn from what he considered multilateral agreements that he found unfavourable to the United States, such as the Trans-Pacific Partnership trade deal.
But the rest of Trump's speech belied that sentiment.
He pointed to the stock market and the employment rate and says the US military will soon be the strongest it has ever been. "Yet in recent years, the United Nations has not reached its full potential because of bureaucracy and mismanagement".