Fears that disruption could widen further to block another sea route sent global oil prices surging in one of the steepest rises of the war.
Brent crude rose more than six per cent, breaking through $US100 a barrel for the first time since May.
The US military late on Thursday said it completed its latest round of strikes on Iran that marked a 13th consecutive night of American attacks.
The trikes lasted more than two hours, according to the US Central Command.
"CENTCOM targeted Iranian military command centres, drone storage facilities, communication networks, coastal surveillance sites and maritime capabilities to further diminish the threat Iran poses to civilian mariners and commercial vessels transiting the Strait of Hormuz," it said in a statement.
Iranian state media said a missile struck Qeshm island on the Strait of Hormuz on Thursday evening, raising the prospect of a further night of attacks in a conflict well into its fifth month that has already killed thousands and raised fears of a global economic downturn.
After the Houthi militia said they had struck the two tankers, Trump said he would hold Iran accountable for any further attacks by the fighters
The Houthi fighters, who control northern and western Yemen, said this week they were imposing a naval blockade on Saudi Arabia, which has diverted millions of barrels of oil per day by pipeline to the Red Sea to get around Iran's blockade of Gulf oil through the Strait of Hormuz.
"If they do this again, the US will hold Iran responsible, in that the Houthis are a Surrogate and/or Proxy of Iran, and major military punishment will be inflicted upon Iran and, of course, the Houthis, themselves," Trump wrote on Truth Social.
He told news outlet Axios he was considering relaunching major combat operations in Iran and was close to a decision.
"They haven't received enough pain yet," Axios quoted Trump as saying.
Sources in Iran and Yemen told Reuters Iran had flown Revolutionary Guard commanders, military advisers and missile- and drone-related equipment into Yemen d Houthi movementyays before the Houthis announced their blockade.
The Houthis dismissed the report.
They said their forces had carried out missile and drone strikes on Saudi oil tankers, the Encelia and the Layla. '
A maritime security source said the Encelia had transmitted a distress call reporting it had been struck by a missile near the Saudi port of Jizan in the Red Sea just north of Yemen late on Wednesday.
Saudi state news agency SPA said the strike had caused a fire at the bow.
Reuters could not immediately confirm the attack on the Layla, or other battlefield accounts, but Trump mentioned two attacks on Saudi tankers.
In the days since they announced their blockade in the Red Sea, several tankers have changed course to avoid the Bab el-Mandeb, heading north instead through the Suez Canal, potentially using a much longer and more expensive route to reach Asian customers by sailing around Africa.
Iran said it attacked US missile systems, weapons and fuel storage sites in Jordan as well as US military posts in Kuwait.
Jordan's army said it engaged four Iranian missiles and six drones in the past 24 hours, intercepting all but one missile, which fell in an uninhabited area.
Iran's Revolutionary Guards said they struck a US electronic warfare unit at Kuwait's al-Adiri base, causing unspecified casualties, in response to an overnight strike on Iran's Shalamcheh border crossing with Iraq.
Neither the United States nor Kuwait has reported casualties at the base.
Iranian military spokesman Brigadier General Mohammad Akraminia said Iran would keep retaliating as long as the US continued to attack its infrastructure and coastal areas, Iranian state TV reported.
