The US president included Iran among "a small group of rogue regimes", and said the US would "totally destroy" North Korea if forced to do so.
Iran's foreign minister said: "Trump's ignorant hate speech belongs in medieval times", and not the UN.
North Korea has yet to respond to the president's threat of destruction.
Mr Trump's speech laid out a vision for a world filled with sovereign states which worked for the betterment of their citizens - but he spent large portions targeting what he called "rogue nations" which are "the scourge of our planet today".
