In a statement on his official website, Khamenei told Trump to "keep dreaming" over the comments on the sites' destruction and questioned the US president's right "to say what a country should or should not have if it possesses a nuclear industry".
In mid-June, Israel launched an unprecedented bombing campaign on Iran. The US briefly joined in, striking key Iranian nuclear facilities.
Last week, during a speech at the Israeli Knesset, Trump reiterated that the US confirmed "obliterating" Iranian nuclear sites during the strikes.
"So we dropped 14 bombs on Iran's key nuclear facilities. Totally as I said originally obliterating them and that's been confirmed," he said.
In a Sunday interview with Fox News, Trump also said Iran "no longer became the bully of the Middle East" after the US strikes which "destroyed their nuclear capability".
He further called the strikes "the most beautiful military operation".
The true impact of the US strikes remains unknown.
The Pentagon has said that the strikes delayed Iran's nuclear programme by between one and two years, contradicting an initial classified US intelligence report that according to American media found the setback was only by a few months.
On Monday, Khamenei called Trump's remarks "improper, wrong, and bullying".
The June war with Israel took place two days ahead of a planned sixth round of nuclear negotiations between Tehran and Washington, which had begun in April.
Nuclear talks have been derailed since with Iran saying it was open to negotiations only if the US provided guarantees of no military action.
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