According to Sky news, Trump stressed the need to work to prevent Iran from acquiring a nuclear weapon, adding: "We must prevent Iran's destabilizing behavior, and we will work to tighten sanctions on Tehran."
Trump blamed the Iranian regime for being behind attacks in various places around the world.
In his speech, the US president touched on US-China relations, calling on Beijing to "respect Hong Kong agreements."
On the economic aspect of relations between Washington and Beijing, Trump acknowledged that the United States lost a large proportion of its factories as a result of Chinese competition.
"We are in a very strong position towards Iran," Trump said ahead of the 74th session of the General Assembly in response to reporters' questions in front of the UN building in New York.
Trump's comments come against the backdrop of rising tensions between the United States and Iran over the recent attack on Saudi oil facilities with Iranian weapons, as well as Tehran's continued interventions in regional affairs.