Araghchi however, suggested that Iran's President Hassan Rouhani would be willing to meet Trump in a multilateral setting if the U.S. returned to the Joint Comprehensive Plan of Action (JCPOA) nuclear deal, which it exited in 2018.
French President Emmanuel Macron, trying to create conditions for talks between the United States and Iran, said he hoped there could be progress on Iran on Tuesday after he held talks with Rouhani on Monday.
The US-Iranian confrontation has ratcheted up since past year, when Trump withdrew from Iran's nuclear deal with major powers and reimposed sanctions that have crippled its economy.
Speaking after arriving in NY yesterday, Mr Rouhani said Iran's message to the world "is peace, stability and also we want to tell the world that the situation in the Persian Gulf is very sensitive".
"Our region is on the edge of collapse, as a single blunder can fuel a big fire", he said, adding that it will become secure only when USA troops withdraw.
Numerous world's leaders have used their speeches so far to defend the multilateralism embodied by the UN at a time when the USA and other nations are sliding toward unilateralism and going it alone.
Tensions in the Middle East have risen as the nuclear deal has unraveled and Iran has turned back to expanding its nuclear enrichment program, despite previous compliance with it for up to a year after Trump's withdrawal from the accord.
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But Rouhani has hinted at only the faintest possibility of a breakthrough. "Our position is for them to take away these preconditions", Rouhani said through a translator on Wednesday.
The U.S. placed new sanctions on Iran last week in response to its attack on Saudi oil facilities.
The shadow of war has lengthened after the air strike on the heartland of Saudi Arabia's oil industry, which included damage to the world's biggest petroleum-processing facility, knocking out more than 5% of global oil supply. "We want a peaceful resolution with the Islamic Republic of Iran".
Rouhani said he had some optimism that the departure of national security adviser John Bolton could change US behaviour, but he had seen "no tangible evidence" of that yet. Trump had already ruled out easing economic pressure and, hours before Rouhani's speech, his administration said it was stepping up sanctions.
Japanese Prime Minister Shinzo Abe and Pakistani Prime Minister Imran Khan both also met with the Iranian and USA leaders.
In a post on his Twitter account on Monday, Iranian Foreign Minister Mohammad Javad Zarif told the three European states that "parroting absurd USA claims" against Iran is "Inconsistent with JCPOA", the official name for the nuclear agreement.
Prospects for a broad pact led by Tehran look unlikely as several of the Gulf Arab states have tense relations with Iran.