President Trump has walked back his announcement of a 20 percent fee to guard the Strait of Hormuz, as missiles continue to fly.

Iran is firing at Jordan ‌and Bahrain after a five-hour US attack on Iranian targets, stepping up a battle that has pushed up oil prices to four-week highs.

US forces carried out waves of ‌attacks for the third night on Tuesday after Tehran said it had closed the Strait of Hormuz.

President Trump’s response to the closure statement was to reinstate a blockade of Iranian shipping and propose charging a 20 per cent fee to guard the waterway.

However, on Wednesday, he said the fee would be replaced by “trade and investment deals that the various Gulf states will be making into the United States”.

Trump said his decision followed highly productive conversations with Middle East leadership and that the investments would be massive, but also “good for them, and their future”.

Iran attacked ‌a US Army base in Jordan with ballistic missiles while Bahrain, which hosts a US naval base, said it had fended off an Iranian aerial attack.

Jordan said it had shot down four ballistic missiles and explosions were heard in Manama, Bahrain’s capital.

Inflation fears

The worsening attacks have increased doubts that a memorandum of understanding signed last month will lead to a permanent halt in the war, which has disrupted global energy supplies and raised fears of a rise in inflation globally.

Regional analysts said the hostilities remained within controlled boundaries for now, with both sides seeking leverage for an eventual peace deal, but that there was still a risk of fighting spinning out of control.

“I doubt the two sides will resume a full war, especially ‌as Trump will suffer – though ‌there is also a distinct possibility that ⁠the Iranians will overplay their hand. That is true of Trump too, of course,” said Yezid Sayigh, a senior fellow at the Carnegie Middle East Center.

Oil prices climb

Oil prices rose again on Tuesday, with Brent crude futures gaining five per cent to hit $US87.49 ($125.24) per barrel – the highest since June 12 but still well below the peak since the war began – before dipping slightly.

The ​war has proved unpopular in the US, where petrol prices have risen since the start of the war and congressional elections are looming in November.

Half of those surveyed in a Reuters poll said they believed the war had not been worth its costs.

The US has said its renewed attacks on ‌Iran are intended to “degrade Iran’s ​ability to attack commercial shipping.”

Iranian media reported US strikes on a number of cities and said four people had been wounded.

Several explosions were heard in Bushehr and Choghadak, according to Fars News Agency, and IRNA quoted a provincial official ​as saying four ‌areas of Bushehr city were hit.

No casualties were reported in Iran’s attack on the US Army base in Jordan.

Hostilities have intensified since Iran said late on Saturday it had closed the Strait of Hormuz after firing a warning shot ​that ​struck a vessel travelling on what it said was an unauthorised route.

Trump said on ​Monday the US was reinstating its blockade of Iranian shipping, which had been lifted as part of the MoU signed ‌last month, and announced the 20 per cent fee on all cargo shipped through it.

Iranian Foreign Minister Abbas Araqchi wrote on X that Tehran was the guardian of the strait and would remain so “forever”, adding in response to Trump: “20 per cent is of course too much. We will be fair.”

Before the war, about a fifth of global oil and gas traffic passed through Hormuz daily. If the US were to impose a 20 per cent fee, it could generate around $US240 million ($344 million) a day.

—with AAP