The top adviser to Mr Khamenei, Mr Ali Akbar Velayati, rejected the United States offer on Tuesday, saying: "Trump's and Pompeo's dream would never come to reality".
"In less than two years, my administration has accomplished more than nearly any administration in the history of our country", Trump said.
"I would like to thank Chairman Kim for his courage and for the steps that he's taken - though more work remains to be done", Mr Trump said, noting existing "sanctions will remain in place until denuclearisation occurs".
Trump also blasted Iran as a "corrupt dictatorship" that is plundering its people to pay for aggression overseas, using his speech to the United Nations General Assembly to threaten more sanctions against Tehran.
Trump saved his harshest rhetoric for the regime in Iran, which he castigated for sowing "chaos, death and destruction" in the Middle East.
"That is why America will always choose independence and cooperation over global governments, control and domination".
President Donald Trump defined Iran in harsh terms during a major address to the United Nations on Tuesday, defending his administration's decision to pull the USA out the controversial 2015 nuclear agreement. Trump met with North Korean leader Kim Jong Un in Singapore on June 12 to discuss efforts to end North Korea's banned nuclear weapons program.
As in his first speech before the U.N. General Assembly, Trump placed importance on the idea of sovereignty and rejected the "ideology of globalism".
"I believe that setting a timetable for all these measures is a task for the second U.S". The "America first" remarks drew on a similar speech he delivered at last year's United Nations, but included more detailed examples of how that vision informs his policies on trade, immigration and the world's hot spots.
A day after the European Union announced a new legal framework in hopes that companies can keep doing business with Iran and evade incoming USA sanctions, Trump demanded that all countries take aim at Tehran - and noted that his decision has been popular among the Shiite-majority nation's Sunni Arab rivals.
Shortly before he was due to address the United Nations general assembly, Trump said: "I'm not meeting with them until they change their tune".
Besides calling out Iran, Trump also criticized China for its trade practices but made no mention of Russia's interference in Syria's war or its suspected meddling in US elections.
Donald Trump has made a personal rapprochement to Hassan Rouhani, saying he was sure that the Iranian president was an "absolutely lovely man". "That was a very risky time", Trump said.
Crude oil prices shot to a four-year high on Tuesday, catapulted by imminent USA sanctions on Iranian crude exports and the apparent reluctance of OPEC and Russian Federation to raise output to offset the potential hit to global supply. The Iranian leader accuses the USA of adopting a hostile stance toward his country.
In the course of discussions with Washington, many European diplomats became convinced that Trump was so determined to kill off the JCPOA because it was the main foreign policy legacy of his predecessor, Barack Obama. "The United States will not be taken advantage of any longer", he said before criticizing "broken and bad trade deals".
He has bucked global convention by relocating the USA embassy in Israel from Tel Aviv to Jerusalem, slashing aid to the Palestinians, and dramatically reducing the number of refugees the US admits from other countries.