US Secretary of State, Mike Pompeo (Picture: PA).
The US Secretary of State, Mike Pompeo, has accused Iran of pursuing "violence and hate", but insisted Washington wants to find a peaceful resolution to tensions between the two countries.
Iran's president, Hassan Rouhani, has warned the Gulf region is on the edge of collapse.
He told the UN in New York there would be no negotiations with the Americans until they returned to the international nuclear deal, which President Trump abandoned.
"Our response to any negotiation under sanctions is negative," he said.
He added, Iran has "resisted the most merciless economic terrorism" from a nation that is engaging in "international piracy".
Iran has turned back to expanding its nuclear enrichment programme after US president Donald Trump's decision last year to pull out of the nuclear deal and re-impose sanctions on Tehran, targeting its ability to export oil.
Mr Rouhani's highly anticipated remarks at the UN came a day after Mr Trump described Iran as "one of the greatest threats" to the planet.
The US has sent military reinforcements and beefed up its security presence in the Middle East in past months amid the rising tensions.
Mr Rouhani went on to say "our region is on the edge of collapse, as a single blunder can fuel a big fire."
His remarks come as the US and its allies accuse Iran of being behind a major drone-and-missile strike on Saudi Arabia's key oil sites earlier this month.
Iran has denied any involvement and says any strikes by the US or Saudi Arabia will lead to "all-out war".
The 14 September attack followed months of lower-level attacks on oil tankers and the shooting down of a U.S. surveillance drone over the Strait of Hormuz. The U.S. and its regional allies blame those attacks on Iran, which it also denies.
Mr Trump, speaking at the UN on Tuesday, left open the possibility of diplomatic engagement with Iran.
That was the same day that Mr Rouhani insisted that he would only consider meeting after sanctions against his country are lifted.
But as he ended his General Assembly speech, Mr Rouhani suggested there was still some room for diplomacy.