At least six people were killed on Tuesday when a cargo ship was hit in the Red Sea by missiles fired by the Houthi militia, Yemen’s government said, an escalation in the chaos that has engulfed shipping in the Middle East.

The Yemeni Transport Ministry said in a statement that the vessel Tihamah was carrying food supplies and was hit while transiting the Bab al-Mandab Strait at the southern entrance to the Red Sea. The ministry added that four crew members — three Pakistanis and one Indonesian — were killed when a fire broke out on board.

Later on Tuesday, the Yemeni Coast Guard said that two members of Yemen’s armed forces were also killed during a rescue mission, when another Houthi missile targeted the vessel.

The Houthi military released a short statement confirming that its forces targeted a ship in the Bab al-Mandab Strait and alleged that the vessel was carrying “Saudi military equipment.” The group has in recent weeks fired on Saudi-linked oil vessels in the Red Sea and said it was imposing a maritime blockade against the kingdom, after deadly clashes with the Saudi-backed government in Yemen.

The deaths on Tuesday mark the first-known fatalities in the Red Sea from Houthi fire since the start of the broader U.S.-Israeli war with Iran in February.

There was no immediate comment from the Saudi, Pakistani and Indonesian governments.

There are conflicting accounts of the ship’s ownership. While the Transport Ministry described the Tihamah as a “Yemeni commercial vessel,” the shipping database Equasis says that it is a small cargo ship owned by an Egyptian company, Thubab for Marine Services, and flies the Tanzanian maritime flag.

The Yemeni government accused the Houthis, an Iran-backed militia based in northern Yemen, of expanding their targets in the Red Sea. “This poses a direct threat to food supplies and consumer goods for millions of Yemenis,” the Transport Ministry said.

The United Kingdom Maritime Trade Operations, which is administered by Britain’s Royal Navy, said Tuesday that a vessel was struck by an unidentified projectile off the Yemeni port of Mokha and that casualties were reported.

The attack threatens to further imperil a crucial maritime transit route. The Red Sea has grown in importance since Iran effectively closed the Strait of Hormuz, a key waterway for oil and gas shipping in the Persian Gulf, at the start of the war.

Saudi Arabia, in particular, has relied on the Red Sea as an alternative export route for its oil, but, last month, the Houthis announced a maritime embargo against the kingdom and have fired on its vessels.

Even so, traffic through the Bab al-Mandab Strait has remained steady. Kpler, a maritime analytics firm, logged 36 vessel crossings on Monday, up one from the day before.

The deadly attack in the Red Sea coincides with a spike in violence in Yemen itself, as the Houthis have carried out missile and drone strikes on government-controlled cities. The Yemeni government has launched counterattacks on rebel forces, and the escalating violence threatens to tip the country back into full-scale civil war.

The two sides have been locked in conflict since 2014, when the Houthis seized the Yemeni capital, Sanaa, with Iranian support. A Saudi-led military coalition intervened the following year to restore the government to power, but a devastating bombing campaign ultimately failed to oust the Houthi rebels.

A United Nations-brokered cease-fire was agreed on in 2022, and the conflict has since been stalemated, leaving Yemen essentially divided in two, with the Houthis controlling the north. Observers now say the truce is close to a breaking point.

In statements posted late Monday, Mohammed Abdulsalam, the Houthis’ chief negotiator, framed the group’s escalating operations in recent weeks as a “legitimate response” to foreign military action. Mr. Abdulsalam accused Saudi Arabia of waging economic war on Yemen during the four-year truce by stopping ships heading to the Houthi-controlled port city of Hodeidah and imposing sanctions on local banks.

Peter Eavis contributed reporting.