Iran's supreme leader Ayatollah Ali Khamenei hailed on Thursday his country's "victory" over Israel and vowed never to surrender to the United States, while claiming that Washington had been dealt a "slap" after striking Iranian nuclear sites, in his first appearance since a ceasefire in the war with Israel took hold.

In a statement and a televised speech carried by state media, Khamenei said US President Donald Trump "exaggerated" the impact of US strikes on Iranian nuclear sites.

"The American president exaggerated events in unusual ways, and it turned out that he needed this exaggeration," Khamenei said.

The United States "has gained nothing from this war," he said, adding that American strikes "did nothing significant" to Iran's nuclear facilities.

By contrast, Khamenei said that Trump had sought to "minimise" the impact of Iran's retaliatory strikes on a US base in Qatar.

Trump "tried... to pretend that nothing had happened, when a major event had occurred", Khamenei said.

The attack "caused damage", while Trump has shrugged it off as "very weak", he added.

"The Islamic republic won, and in retaliation dealt a severe slap to the face of America," he said, a reference to Iran's missile launch targeting the largest US base in the Middle East.

Khamenei also threatened to carry out more strikes on US bases in the region if Iran came under another attack by the United States.

"The Islamic republic has access to important US bases in the region and can act against them whenever it deems it necessary," said Khamenei.

"It can happen again in the future; if an attack occurs, the cost to the enemy and the aggressor will certainly be high."

"I want to congratulate the great Iranian nation... for its victory over the fallacious Zionist regime," he added, claiming that Israel had "almost collapsed" because of Iran's strikes.

Khamenei's remarks come two days after a ceasefire ended a 12-day war between Iran and Israel, the foes' deadliest and most destructive confrontation in history.

It also follows a stinging row in the United States over the actual extent of the damage inflicted by American strikes on key Iranian nuclear sites during the conflict.

Both Iran and Israel had already claimed they won, with Israeli Prime Minister Benjamin Netanyahu hailing on Tuesday a "historic victory" for Israel.