The attacks, in the Gulf of Oman leading to the strait and at the entrance to the Red Sea - both vital choke points for global oil supplies - come as the war shows no signs of ending despite repeated assertions from US President Donald Trump of a deal being imminent.
Oil prices gained and global shares retreated amid renewed pessimism about a quick end to the conflict.
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, which said in July it would impose a naval blockade on Saudi Arabia in the Red Sea, attacked a Saudi ship they said was 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 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 ship ignored repeated warnings to stop violating a naval blockade on Iranian ports, the US Central Command said.
Maritime sources told Reuters the ship was hit off Pakistan while sailing into the Gulf of Oman.
Both Iran and the United States have stepped up rhetoric in the past two days.
Iran's top security official, Mohsen Rezaei, said on Tuesday that the vital Strait of Hormuz shipping route would remain closed unless the US accepted Iran's conditions to end the war: the release of Iran's frozen assets and an end to conflicts throughout the region, including in Lebanon and Gaza.
That followed a new demand from Trump on Monday that Iran should pay compensation for people killed in 50 years of wars, attacks and protests.
Trump has repeatedly alternated between threats of escalation and claims that a peace deal is imminent for the conflict that began when the US and Israel launched attacks on Iran on February 28.
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."
The comments from Rezaei, appointed on Sunday as second-in-command of the body that co-ordinates Iran's security and foreign policy, are the strongest indication the Strait of Hormuz will not reopen to shipping soon.
The waterway handled a fifth of global oil and liquefied natural gas flow before the war.
"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.
