Iran has said it will keep the Strait of Hormuz closed until the United States ends the war, releases frozen Iranian assets and accepts a region-wide ceasefire, as deadly attacks pushed the shipping crisis into two other strategic waterways.

“America must end the war, return Iran’s frozen assets, and the war must end across the region, including Lebanon and Gaza,” Mohsen Rezaei, secretary of Iran’s Supreme National Security Council, said on Tuesday.

Rezaei said Tehran had passed its conditions to Washington through mediators. The United States did not immediately respond publicly to his remarks.

His statement followed more optimistic comments from Pakistan’s defence minister, Khawaja Asif, who told Bloomberg that Washington and Tehran appeared close to “some sort of an arrangement”.

“Things are shaping up again in favour of a peace arrangement or a deal,” Asif said, adding that signals over the previous two or three days suggested an agreement was near. Pakistan, Oman and Qatar have been involved in mediation.

At the southern entrance to the Red Sea, six people were killed in an attack on the Tihamah near Yemen’s Bab el-Mandeb Strait, according to Yemeni authorities.

Yemen’s transport ministry said three ballistic missiles struck the commercial vessel, which it said was carrying food. Four crew members — three Pakistanis and one Indonesian — were killed, and four others were wounded.

The Yemeni Coast Guard said two members of the National Resistance Forces, an anti-Houthi group involved in the rescue, were also killed when the Houthis attacked again after emergency crews arrived. Ten people were wounded in total, including seven crew members and three rescuers, according to the Coast Guard.

Pakistan’s deputy prime minister and foreign minister, Ishaq Dar, confirmed on Wednesday that three Pakistani citizens had been killed and one injured. He condemned what he called a Houthi attack on a non-combatant commercial vessel and said Pakistan was working with Saudi and Yemeni authorities to repatriate the victims’ remains.

The Houthis later said they had attacked an unnamed Saudi ship carrying military equipment in Bab el-Mandeb. They did not identify it as the Tihamah. Ship data cited by Reuters listed Egyptian companies as the Tihamah’s owners and managers, while maritime security firm Ambrey said it was neither Saudi-owned nor Saudi-operated.

UK Maritime Trade Operations reported that a cargo vessel in the area had been hit by an unknown projectile. Reuters verified images of the damaged Tihamah and ship-tracking data placing it near Murad, Yemen, on 11 August.

In the Gulf of Oman, US Central Command said an MH-60 naval helicopter fired two Hellfire missiles into the engine room of the Panama-flagged Vela Nova, disabling its steering gear as it sailed towards an Iranian port.

The command said the civilian crew had ignored repeated warnings and accused the vessel of violating the US blockade of Iranian ports. Casualties from the strike had not been confirmed.

The attacks affected both approaches to a maritime route that carried about a fifth of global oil and liquefied natural gas before the war. Shipping data published on Wednesday showed eight vessels tracked through Hormuz on Tuesday, the lowest daily count in a week and well below the roughly 130 to 140 daily transits recorded before Iran closed the waterway after US-Israeli attacks began on 28 February.