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Donald Trump would “absolutely” consider a new military strike on Iran’s nuclear facilities, he said on Friday, as he lashed out at Ayatollah Ali Khamenei.

The president’s comments came at a White House press conference just six days after the US bombed Iranian nuclear sites in a mission Trump said had “obliterated” the country’s atomic weapons programme.

Asked in the White House if he would consider a new attack on Iran’s nuclear sites if intelligence concluded that Tehran was able to keep enriching uranium to levels that concerned the US, Trump responded: “Sure, without question, absolutely.”

He was speaking after intelligence reports suggested the American attack on the Natanz, Isfahan and Fordow nuclear sites called into question his claim that the bombardment had destroyed the facilities.

Trump also attacked Khamenei, Iran’s supreme leader, in a lengthy post on social media, saying he had “so blatantly and foolishly” claimed victory in the “war with Israel”.

Khamenei said on Thursday that the US strikes on Iran’s nuclear sites “did not achieve anything”, adding to conflicting assessments of the damage from the American bombing raid last week.

The back-and-forth also comes just days after Iran launched missiles at a US military base in Qatar in what Trump said was a “very weak response” to “the obliteration of their nuclear sites”.

Trump had “exaggerated because he needed to”, Khamenei said. “Anyone who heard his remarks could tell there was a different reality behind his words — they could do nothing,” the supreme leader said in his first public comments since a ceasefire with Israel took hold this week.

Trump also said that had stopped Israel, or the US military, from assassinating the 86-year-old Iranian leader.

“I SAVED HIM FROM A VERY UGLY AND IGNOMINIOUS DEATH,” Trump said of the Iranian leader. “I wish the leadership of Iran would realize that you often get more with HONEY than you do with VINEGAR. PEACE!!!”

The president’s warning that the US could attack again will add to the questions about the state of Iran’s nuclear programme following the bombardment.

An early assessment by the Pentagon’s Defense Intelligence Agency concluded that they could be rebuilt within six months. Preliminary intelligence assessments provided to European governments also indicated that Iran’s highly enriched uranium stockpile remained largely intact, the Financial Times reported this week.

John Ratcliffe, the director of the CIA, said in a statement that Iran’s nuclear programme had been “severely damaged” and “several key Iranian nuclear facilities were destroyed and would have to be rebuilt over the course of years”.