US President Donald Trump has lashed out at critics of his agreement with Iran, calling those who accused him of offering concessions to end the war "fools" ahead of negotiations in Switzerland on implementing the deal.

In a sudden development after uncertainty over when the deal agreed earlier this week would be formally signed, Trump put his name to it in thick black ink at a candlelit dinner with French President Emmanuel Macron at the Palace of Versailles outside Paris on Wednesday.

Macron, for whom the signing at the palace, which hosted the signing of the treaty that ended World War I, was an immense coup following his hosting of the G7 summit, shouted "bravo" as Trump signed.

"These fools, who think I haven't been tough enough on Iran when the stock market just hit a high and oil prices are 'tumbling' down, are either jealous, bad people, or stupid," Trump posted on social media on Thursday, hours after signing the deal.

Oil prices tumbled after Trump and his Iranian counterpart separately signed their accord to end the Middle East war, with the Strait of Hormuz to reopen, but two months of negotiations lie ahead.

Prime Minister Shehbaz Sharif of Pakistan, who also helped mediate the agreement, said it "shall enter into force with immediate effect", and Iran "will instantly reopen the Strait of Hormuz". He also signed the accord.

A two-month negotiating period now begins with all eyes on the reopening of Hormuz and whether progress can be made in talks over Iran's nuclear programme.

Macron hailed the deal "which allows for peace, the reopening of the Strait of Hormuz without tolls, and 60 days to conclude an agreement on nuclear, ballistic, and regional activities".

There remained confusion over the next steps, with the accord originally supposed to have been signed at an exclusive mountain-top resort in Switzerland on Friday by Iran's chief negotiator and parliament speaker, Mohammad Bagher Ghalibaf, and US Vice President JD Vance.

Iran’s foreign ministry spokesperson Esmaeil Baqaei said an in-person ceremony was no longer needed.

But Sharif said an official ceremony will take place on Friday in Switzerland, and technical talks will commence.

Under the text, Washington commits to immediately waiving oil sanctions crippling Iran's economy.

Trump's decision to end the war, in which 13 US service members were killed and a vast proportion of US ammunition stockpiles was used, has unsettled some of his allies at home.

But US Senator Bill Cassidy from Trump's Republican Party described it as the "worst foreign policy blunder in decades".

"Iran's nuclear ambitions were not curbed, and they have learned that threatening the Strait of Hormuz works," he said.

Fox News cited critics who said the agreement gave Iran "huge financial benefits" without requiring the dismantlement of its nuclear programme.