Trump stated in an interview with Fox Business News on Friday that he sent a letter to Khamenei to initiate negotiations with Iran.
He allegedly wrote that military action could be considered if negotiations fail.
Hopefully, we can get a peace agreement. I'm not speaking from a position of strength or weakness. I'm just saying that I prefer a peace agreement to the other option. But the other option will solve the problem, Trump told journalists who asked about the letter on Friday.
"The goal is dominance"
Ali Khamenei says he does not believe the purpose is problem-solving.
Some bullying governments – the only term I can think of for some foreign figures and leaders is bullying – insist on negotiations. But their negotiations do not aim to solve problems, but the goal is dominance, says the ayatollah without directly mentioning Trump or the letter.
According to the ayatollah, the US wants to impose military demands on Iran and link them to issues affecting the country's regional influence.
Meanwhile, Iran's Foreign Minister Abbas Araghchi said on Saturday that the Iranian government had heard about the letter "but not received anything". On Friday, Araghchi told AFP that Trump should tone down his rhetoric.
We will not engage in direct negotiations with the US as long as they continue their approach with maximum pressure and threats, he said.
Has warned Iran
The UN, on the other hand, welcomes Trump's outstretched hand.
"As a principle, we confirm that diplomacy is still the best way to ensure a peaceful character of Iran's nuclear program", says spokesperson Stéphane Dujarric in a comment.
"In that regard, we welcome all diplomatic efforts towards that goal", he continues.
The news about Trump's letter comes after both the US and Israel warned that they will never allow Iran to develop nuclear weapons, which has led to fears of a military conflict with Tehran.
Trump unilaterally withdrew the US from an agreement with Tehran on nuclear technology from 2015 during his first term as president.