New attacks on shipping were reported in the Gulf of Oman and Red Sea amid the Iran war.
Iran said the Strait of Hormuz would remain closed unless the US accepted its conditions.
Trump and Iranian officials exchanged tougher rhetoric as prospects for ending the war dimmed.
New attacks on shipping in the Gulf of Oman and the Red Sea on Tuesday added to concerns that the Iran war could drag on, as Tehran said the Strait of Hormuz would remain closed unless Washington accepted its conditions for ending the conflict.
The attacks came as prospects for ending the Iran war appeared to dim, despite repeated assertions by US President Donald Trump that a deal was imminent. The Gulf of Oman and Bab el-Mandeb Strait are key maritime chokepoints for global oil supplies. Oil prices rose and global shares retreated amid renewed pessimism over a quick end to the conflict. Reuters reported that Brent crude futures settled 1.4% higher at $88.91 a barrel, while US crude rose 1.3% to $83.20.
At the southern end of the Red Sea, four crew members were killed in a suspected Houthi attack on a small cargo vessel in the Bab el-Mandeb Strait on Tuesday, Yemen's Transport Ministry said. Two Yemeni rescuers from an anti-Houthi military group were also killed, Yemen's Coast Guard said.
The fatalities aboard the Egyptian-owned Tihamah, if confirmed, would be the first deaths on shipping by Yemen's Iran-aligned Houthis since the Iran war began.
The Houthi-run news agency Saba reported that the group had attacked a Saudi ship carrying military equipment in the Bab el-Mandeb Strait. It did not name the ship, and there was no immediate Saudi response to the report. The Houthis said last month they would impose a naval blockade on Saudi Arabia in the Red Sea.
The US military, meanwhile, said a US Navy MH-60 helicopter fired two Hellfire missiles to disable the steering gear of a Panama-flagged cargo ship.
The US Central Command said the ship had ignored repeated warnings to stop violating a naval blockade on Iranian ports. Maritime sources told Reuters that the ship was hit off Pakistan while sailing into the Gulf of Oman.
Hormuz Stand-off Deepens
The incidents came as Iran and the United States stepped up their rhetoric over the past two days.
Iran's top security official, Mohsen Rezaei, said on Tuesday that the Strait of Hormuz would remain closed unless the US accepted Iran's conditions for ending the war. These include the release of Iran's frozen assets and an end to conflicts throughout the region, including in Lebanon and Gaza.
"As long as America does not change its behaviour and does not accept Iran's conditions, the Strait of Hormuz will not be opened," Rezaei said, according to the semi-official Tasnim news agency.
Rezaei, appointed on Sunday as second-in-command of the body that coordinates Iran's security and foreign policy, made the remarks after Trump on Monday demanded that Iran pay compensation for people killed in 50 years of wars, attacks and protests.
Throughout the conflict, Trump has alternated between threats of escalation and claims that a peace deal is imminent.
In an interview released late on Monday, he suggested the uncertainty could last for a while, saying he might just "bop along" and let Tehran fail economically, or hit them "really, really hard."
"I'm sort of negotiating," Trump told Real America's Voice. "They're very devious negotiators."
Speaking to reporters after a visit to Ohio on Tuesday, Trump said "Iran is going fine, going just absolutely fine."
"We totally control the Strait of Hormuz ... Nobody else, only us," he said.
"At some point, maybe they'll do something and then they get blown away," he said of Iran. "But right now, we're in a very good position. We have a country that has been the bully of the Middle East for 50 years, really 51 if you think about it ... and they're no longer the bully of the Middle East."
Asked about an incident in which he switched planes in Turkey last month because of worries over reports of a potential Iranian assassination threat, Trump suggested the alternative aircraft may have faced greater risk.
"That would be the plane I think that they would be more likely to go for," he told reporters after The Washington Post broke the story about him secretly taking a military flight instead of Air Force One in an operation involving him being moved between aircraft in a catering truck.
"Any consequential president has a lot of threats," Trump added. "I don't worry about anything."
Rezaei's comments were the strongest indication that the Strait of Hormuz would not reopen to shipping any time soon. The waterway handled a fifth of global oil and liquefied natural gas flows before the war.
There was no immediate comment from Washington on Iran's latest comments.
According to Reuters, thousands of people have been killed in the conflict since the US and Israel launched attacks on Iran on February 28. Iran has struck US assets and infrastructure in countries including Oman, Jordan, Kuwait, Israel, the United Arab Emirates and Saudi Arabia.
Raising the prospect of further escalation, Mohammad Reza Naqdi, an adviser to the commander of Iran's Revolutionary Guards, said on Iranian state television on Tuesday that the corps was developing the ability to carry out operations "on enemy soil."
"We need to be able to move the operations to the enemy's soil, whenever this is needed and ordered," he said. "This is the characteristic of the offensive doctrine that has to be attained."
