US airstrikes did not destroy Iran's nuclear capability and only set it back by a few months, according to a preliminary US intelligence assessment, as a shaky ceasefire brokered by US President Donald Trump took hold between Iran and Israel.

Earlier on Tuesday, both Iran and Israel signalled that the air war between the two nations had ended, at least for now, after Trump publicly scolded them for violating a ceasefire he announced at 0500 GMT.

As the two countries lifted civilian restrictions after 12 days of war - which the US joined with an attack on Iran's uranium-enrichment facilities - each sought to claim victory.

Trump said over the weekend that the US deployment of bombs had "obliterated" Iran's nuclear programme.

But that claim appeared to be contradicted by an initial assessment by one of his administration's intelligence agencies, which suggested Iran's enriched uranium stocks had not been eliminated, and the country's nuclear programme, much of which is buried deep underground, may have been set back only a month or two.

Iran says its nuclear research is for civilian energy production.

The White House said the intelligence assessment was "flat out wrong."

Trump's administration told the United Nations Security Council on Tuesday that its weekend strikes on Iranian nuclear facilities had "degraded" Iran's nuclear programme, short of Trump's earlier assertion that the facilities had been "obliterated."

Israeli Prime Minister Benjamin Netanyahu said on Tuesday that the attack on Iran had removed the threat of nuclear annihilation and was determined to thwart any attempt by Tehran to revive its weapons programme.

Iranian President Masoud Pezeshkian said his country had successfully ended the war in what he called a "great victory," according to Iranian media.

Pezeshkian also told Saudi Crown Prince Mohammed bin Salman that Tehran was ready to resolve differences with the US, according to official news agency IRNA.

Israel launched the surprise air war on June 13, attacking Iranian nuclear facilities and killing top military commanders in the worst blow to the Islamic Republic since its war with Iraq in the 1980s.

Iran, which denies trying to build nuclear weapons, retaliated with barrages of missiles on Israeli military sites and cities. (Reuters)