Iran live updates: Hegseth estimates war with Iran cost the US $37.5 billion

Even the threat of attacks by the Houthis is having an impact on ships transiting through the Bab el Mandeb route -- a strait in the Red Sea's southern gateway and one of the world's most important oil shipping routes for crude and fuel shipments moving between the Middle East, Europe and Asia -- according to a ship fleet company executive who has seven tankers in the region.

"There is no transit through the Strait of Hormuz. Also as of today the Bab el Mandeb transits into the Red Sea are also uncertain as Houthis have sent messages to many companies banning transit to Saudi ports," the executive told ABC News.

"We deal with uncertainty on a daily basis but the level of uncertainty now is unprecedented. Especially for the seafarers this is a nightmare. This is a huge concern for the world because if the Bab el Mandeb closes while the Strait of Hormuz is closed oil will go to 150!" the executive said.

The executive said it is "too risky" to go through the Arabian Gulf, adding that the "Red Sea transit has become an unknown. No incidents as yet but clear threats and instructions from Houthis not to head to/from Saudi ports."

-ABC News' Desiree Adib

President Donald Trump insisted on Tuesday that Iran "desperately" wants to meet for ceasefire talks despite the U.S. and Iran exchanging limited strikes for over a week.

But, Trump maintained that the war is not yet over telling reporters at the White House, "We're not finished."

"We're not leaving," Trump said.

Multiple crew members were injured in Iranian strikes on a Kuwaiti tanker passing through the Strait of Hormuz on Monday evening, Kuwait’s foreign ministry said in a statement on Tuesday.

The ministry said it had summoned Iran’s ambassador to Kuwait to protest the alleged attack.

"The State of Kuwait renewed its demand for Iran to immediately cease its illegitimate attacks, emphasizing Kuwait's reservation of its right to take necessary measures, and holding Iran fully responsible for this aggression and its ongoing assaults against the State of Kuwait," Kuwait's Ministry of Foreign Affairs said in a statement Tuesday.

The Pentagon on Tuesday identified the soldier killed in Iraq over the weekend during the disposal of a downed Iranian one-way attack drone.

Army Sgt. Michael Emmanuel Swinton, 30, of Fayetteville, North Carolina, died during the controlled detonation of the drone at Erbil Air Base, Iraq, the Pentagon said.

Swinton was assigned to D Battery, 2nd Battalion, 55th Air Defense Artillery Regiment, 108th Air Defense Artillery Brigade, Fort Bragg, North Carolina.

At least 17 U.S. troops have been killed since the U.S. and Israel launched attacks against Iran on Feb. 28, while some 500 others have been wounded, according to Defense Department figures and an updated casualty count provided by Pentagon spokesman Sean Parnell on Monday.

One service member also remains missing following last week's attack in Jordan, where officials are still working to identify human remains recovered at the scene.

-ABC News' Steve Beynon