State Department tells Americans worldwide to 'exercise increased caution'

Adm. Brad Cooper, the head of U.S. Central Command, provided an update on Saturday as the U.S. war in Iran entered its fourth week.

Cooper, in a video message, said the U.S. military has struck 8,000 military targets, including 130 Iranian vessels.

"Their Navy is not sailing, their tactical fighters are not flying and they have lost the ability to launch missiles and drones at the high rates seen at the beginning of the conflict," Cooper said. "Our progress is obvious."

Addressing Iran's blockade of the Strait of Hormuz, Cooper said the U.S. dropped "multiple 5,000-pound bombs" on an underground weapons storage facility on Iran's coast in an effort to degrade it's military capabilities in the crucial shipping lane.

"My operational assessment continues to be Iran's combat capability is on the steady decline as our offensive strikes ramp up," he said.

Iranian media is reporting that U.S.-Israeli strikes again targeted Iran's Natanz nuclear facility Saturday morning.

No leakage of radioactive materials has been reported in the complex and there is no danger to residents in the surrounding area, according to social media posts by the Iranian judiciary's Mizan News Agency and Iran's semiofficial, IRGC-affiliated Tasnim News Agency.

CENTCOM declined to comment on this or provide details. ABC News has reached out to the Israel Defense Forces.

Earlier this month, the International Atomic Energy Agency (IAEA) -- the nuclear watchdog of the United Nations -- confirmed that entrances to Iran's underground and previously bombed uranium-enrichment plant at Natanz had been recently damaged by the U.S.-Israeli strikes on the country.

-ABC News' Morgan Winsor

Airstrikes by Israel and the United States against Iran will "increase significantly" in intensity, Israeli Defense Minister Israel Katz said Saturday.

"This week, the intensity of the attacks that the IDF and the U.S. military will carry out against the Iranian terrorist regime and against the infrastructures on which it relies will increase significantly, and the campaign led by U.S. President Donald Trump and Israeli Prime Minister Benjamin Netanyahu will continue," Katz said in remarks at an military operations center in Tel Aviv.

"We are determined to continue leading the attack against the Iranian terrorist regime, to behead its commanders and thwart its strategic capabilities -- until all security threats to the State of Israel and U.S. interests in the region are removed," Katz said. "We will not stop until all war goals are achieved."

-ABC News' Dana Savir

President Donald Trump said Friday he's considering "winding down" military efforts in the Middle East amid the ongoing war in Iran, claiming his administration is getting "very close" to meeting their objectives there.

Those objectives, Trump outlined in a social media post Friday, include "completely degrading" Iran's missile capability; eliminating Iran's navy and air force; "destroying" its defense industrial base; "never allowing Iran to get even close to Nuclear Capability"; and protecting the U.S.' Middle Eastern allies, including Israel, Saudi Arabia, Qatar, the United Arab Emirates, Bahrain and Kuwait.

The president did not make clear how the U.S. military has materially achieved his objectives.

Trump also said that the Strait of Hormuz will need to be "guarded and policed, as necessary, by other Nations who use it" -- making clear that the U.S. does not use the strait, but also that he'd "help" the countries that do with "their Hormuz efforts."

He appeared to pass off the responsibility of opening the strait to other nations, without making clear which ones.

"If asked, we will help these Countries in their Hormuz efforts, but it shouldn't be necessary once Iran's threat is eradicated. Importantly, it will be an easy Military Operation for them," Trump wrote.

-ABC News' Isabella Murray