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

Secretary of State Marco Rubio told reporters that Iran is continuing to send messages "directly and through multiple channels with other countries," indicating it was willing to negotiate, and that the U.S. remains open to diplomacy -- but he noted that a "growing split" in Iran’s system complicates that.

"So, they’ll have to work out that split internally. We’re going to continue to respond," he said.

Rubio said the current military mission is solely focused on responding to Iran’s attacks in the Strait of Hormuz.

"The only reason why the U.S. is conducting strikes is against assets of Iran that are being used to attack global commercial shipping," Rubio said. "Other countries should join us in this effort, but the United States is involved not just in protecting those ships but in targeting the places that they use to launch these missiles and drones."

Rubio also spoke about the service members killed.

"The mission they carry out is very, very dangerous," he said. "Our hearts go out to the families of the heroes that paid the ultimate price."

-ABC News’ Shannon Kingston

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