In his debut speech to the body in New York, he warned America would destroy North Korea if it was forced to defend itself or its allies.
He mocked North Korea's leader, Kim Jong-un, saying: "Rocket man is on a suicide mission."
North Korea has tested nuclear bombs and missiles in defiance of the UN.
Iran, Mr Trump said, was a "corrupt dictatorship" intent on destabilising the Middle East.
He called on the government in Tehran to cease supporting terrorism and again criticised the Obama-era deal over Iran's nuclear programme, which he called an embarrassment.
In other parts of his speech:
He said the crisis in Venezuela, which is led by a leftwing government hostile to the US, was "unacceptable" and the America could not "stand by and watch"
He denounced socialism as an ideology, saying it had only brought "anguish and devastation and failure"
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