Iran live updates: Trump says Iran 'desperately' wants to meet for ceasefire talks amid new strikes

President Donald Trump said the U.S. hit Iran "hard" in honor of the U.S. service members who were killed by Iran over the weekend.

U.S. Central Command said two service members were killed in an attack on Jordan on Friday, and that a third service member remained missing. Another service member was killed in Iraq on Saturday, CENTCOM said.

Trump said on Sunday the U.S. lost "great patriots," but said the mission of ending Iran's nuclear capabilities would carry on -- claiming that U.S. forces started another wave of attacks against Iran "in honor" of the service members lost.

"Well, we feel very badly, but you know those great people, those great patriots, were out there fighting that Iran cannot have a nuclear weapon. Iran has been very, very badly damaged," Trump told reporters after flying back from the World Cup final in New Jersey.

"We hit them very hard again tonight, and we did that in honor of the probably three -- It's probably three as opposed to two. Great patriots," Trump said.

-ABC News' Devin Garbitt and Isabella Murray

Mohammad Bagher Ghalibaf, the speaker of the Iranian parliament and the leader of Tehran's peace talks delegation, said in a statement posted on social media on Monday that "Americans keep bringing new military equipment to the region and claim they're after stopping the war."

Iran, Ghalibaf added, is ready to face the U.S.

"We've reached the stage of mastery in recognizing these American games, and on that basis, we've prepared ourselves. Actions must confirm claims, not contradict them," he wrote.

-ABC News' Victoria Beaule

The Pentagon on Monday identified two soldiers killed in Friday's Iranian missile and drone attack on Muwaffaq Salti Air Base in Jordan.

Among them was Pvt. Isabella Gonzales, 19, of Carrollton, Texas, the Pentagon said. Gonzales was assigned to 1st Battalion, 57th Air Defense Artillery Regiment, 52nd Air Defense Artillery Brigade, 10th Army Air Missile Defense Command, Ansbach, Germany.

1st Lt. Tyler James Feehan, 25, of Ewa Beach, Hawaii, died on July 18, from wounds sustained in the attack the day before. Feehan was assigned to 2nd Battalion, 55th Air Defense Artillery Regiment, 32nd Army Air Missile Defense Command, Fort Bragg, North Carolina, the Pentagon said.

A third U.S. service member remains missing following the attack. U.S. Central Command, which oversees troops in the Middle East, said human remains recovered at the scene are undergoing identification.

Separately, another U.S. service member was killed in Iraq on Saturday in an incident involving the disposal of a downed Iranian drone, according to CENTCOM.

The Pentagon typically withholds the identities of deceased troops until at least 24 hours after their next of kin have been notified.

-ABC News’ Steven Beynon

The U.K. Maritime Trade Operations Centre reported that a vessel was on fire in the southern route area of the Strait of Hormuz on Monday morning, near Oman's coast.

The vessel "was struck by an unknown projectile," the UKMTO said in its report. "The crew safely abandoned the vessel and have been recovered by a tug boat. The fire has not been extinguished and the vessel is currently adrift. There is no reported environmental impact."

-ABC News' Victoria Beaule