The escalating attacks threatened to derail efforts to end the war, with Trump warning that Tehran would "pay the price" for stalled negotiations.
US Central Command said in a social media post the military is striking "multiple targets in Iran" and it's being done "in response to Iran's unwarranted and continued aggression."
Speaking to reporters after being briefed by commanders at Central Command headquarters in Florida, Hegseth said Iran had been given a chance to make a deal but had not taken it.
"We will hit them hard on our terms on the targets that improve the environment for us to operate in and undermine the capabilities that Iran wants to have," Hegseth said.
Hours earlier, Trump said the US would attack Iran despite a ceasefire, in place since April, and his efforts to reach a deal to end the war.
"We hit them hard yesterday, and we're going to hit them again hard today," Trump had told reporters.
The strikes come a day after the US hit Iran following the crash of an Army helicopter near the Strait of Hormuz that Trump blamed on the Islamic Republic.
Earlier Trump revealed the United States has been taking oil out of Iran.
"I'm just announcing today for the first time, but we've been taking out millions of barrels of oil, millions of barrels every night," Trump said, adding that Iran "just figured it out".
"Millions of barrels of oil has come out, and that's why it's at $US85-90 a barrel, instead of $US250," Trump said, sharing no other details about these operations.
He later said more than 100 million barrels of crude had passed through the Straits of Hormuz as part of what he called a secret US mission to support oil tankers.
"More than 200 Commercial Ships have safely travelled through the Strait," he said in a post on Truth Social.
Trump said the United States is still looking to make a deal.
"We want a deal that is meaningful, we want a deal that works," Trump added about the negotiations with Iran.
Trump said Iran has already agreed to not obtaining a nuclear weapon but the agreement still needs to be signed.
Meanwhile, the United Nations nuclear watchdog's 35-country Board of Governors passed a US-backed resolution telling Iran to declare its remaining enriched uranium stocks and let inspectors verify them.
The move came within hours of the US and Iran trading military strikes.
Israeli and US attacks in June of last year destroyed or badly damaged Iranian uranium-enrichment plants but much of the enriched uranium they produced, including material close to weapons-grade, is thought to have survived.
Iran still has not informed the International Atomic Energy Agency of the fate of that material, or let IAEA inspectors return to the bombed sites to check.
The US led the push for the resolution but Iran has called it "whitewashing military aggression" since inspectors had access before the strikes.
The resolution text submitted by the US, United Kingdom, France and Germany was passed with 21 votes in favour, three against and 10 abstentions, diplomats at the closed-door meeting said.
The countries opposing were Russia, China and Niger, they said.
Iran's mission to the IAEA had warned the board to be "cautious on the path forward".
with AP and DPA
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