Brent crude climbed above US$96 a barrel on Thursday, its highest in six weeks, as the United States struck Iran for an 11th consecutive night and President Donald Trump warned that Washington would destroy an Iranian bridge or power plant for every attack on shipping in the Strait of Hormuz.

The overnight strikes followed Iranian attacks on Tuesday against US assets in Kuwait, Bahrain and Jordan and a vessel in the strait, according to US military accounts reported by CBS and CNN. Trump set out the new rule on Wednesday: one Iranian bridge or power plant hit for each Iranian strike on a tanker. He did not name the targets.

The Pentagon has confirmed 18 US service members killed since the fighting escalated in early July. On Wednesday Trump travelled to Dover Air Force Base in Delaware for the return of four soldiers' remains, after meeting their families. Iran has kept up its own strikes on US bases across Jordan, Iraq, Kuwait and Bahrain.

Defence Secretary Pete Hegseth put the cost of the war to the United States at US$37.5 billion so far, with the Pentagon seeking more from Congress.

Diplomacy is still behind the fighting. A 10-day ceasefire proposal from Qatar, Egypt and Pakistan sat unanswered on Thursday, and Secretary of State Marco Rubio said Iran was not serious about talks. The dispute turns on the wording of a June memorandum over who controls passage through the strait: Iran claims a residual authority over the waterway, and the US says the agreement requires it to stay open. A 60-day truce signed in June had collapsed within weeks.

The maritime picture worsened through the week. The Greek-operated tanker Kavomaleas, managed by Dynacom, was struck by a projectile and set alight near Limah, off Oman, inside the strait on Tuesday, the UK Maritime Trade Operations agency reported, and a second tanker was also reported hit. About a fifth of the world's seaborne oil moves through the strait, which Iran has declared closed.

On Thursday the danger reached a second waterway. The same UK agency reported a tanker struck by a projectile about 70 nautical miles off Saudi Arabia's Red Sea coast, and Houthi forces in Yemen were reported to have attacked two Saudi tankers there, the first hits on that alternative export route.

For Australians the conflict reaches the airport and the bowser. The Department of Foreign Affairs and Trade tells travellers not to go to Iran, Iraq, Lebanon, Syria, Yemen and the Palestinian Territories, and to reconsider any need to travel to Qatar, the United Arab Emirates, Bahrain, Israel and Kuwait. The European aviation regulator has told airlines to avoid Gulf airspace until at least 29 July. Australia's own part is limited and defensive: an E-7A Wedgetail surveillance aircraft and crew in the United Arab Emirates, and air-to-air missiles supplied to the Emirates, with Prime Minister Anthony Albanese having ruled out sending troops into Iran.

As of Thursday the strikes were continuing, the strait remained closed by Iran's declaration, and the mediators' proposal was unanswered. Crude sat at its highest since mid-June, and the cost was moving toward Australian petrol pumps just as the last of the government's fuel excise relief runs out at the start of August.