President Donald Trump said Monday that the United States will become the "guardian" of the Strait of Hormuz as the U.S. and Iran continue exchanging strikes and publicly spar over control of the critical shipping lane.

During an interview on Fox & Friends, Trump said the U.S. intends to keep the waterway open but argued that allied nations should pay for America's role in protecting it.

"We're going to keep the strait, and we'll probably run it," Trump said.

He added, "We'll become the guardian of the strait. Maybe we'll become the guardian angel of the strait, and we should be reimbursed for that. When we do that we're going to be reimbursed because the other nations are very wealthy, they're on our side, and we can't be expected to do that for nothing unlike we had for many years."

Trump also said the U.S. has protected the waterway for decades without compensation.

"We guarded the strait for 50 years, and we never got paid for it," he said. "We guarded it for nothing."

His comments came a day after U.S. Central Command (CENTCOM) announced it had carried out another round of strikes against Iran.

According to CENTCOM, U.S. forces struck "dozens of targets at multiple locations with precision munitions to degrade Iran's ability to continue attacking international shipping flowing through the Strait of Hormuz."

The military also pushed back on Iran's claims over the strategic waterway.

"The Strait of Hormuz is a vital maritime corridor for global trade. Iran does not control it," CENTCOM said. "U.S. forces are postured and prepared to ensure that freedom of navigation remains available to commercial shipping despite Iran's continued unwarranted aggression, harassment, threats, and arbitrary declarations."

Iran quickly responded. According to The Associated Press, the Islamic Revolutionary Guard Corps said, "The Strait of Hormuz is our territory, and we will not allow a rogue and child-killing army from the other side of the world to continue its illegal interference in it."

The latest exchange follows a third round of U.S. strikes against Iran after an Iranian attack on a container ship in the Strait of Hormuz, further raising tensions over one of the world's busiest and most strategically important shipping routes.