The mission, called Operation Midnight Hammer, involved decoys and deception, and met with no Iranian resistance, Mr Hegseth and US Air Force General Dan Caine, chairman of the Joint Chiefs of Staff, said at a Pentagon news conference on Sunday.
Mr Hegseth said it is important to note the US strikes did not target Iranian troops or the Iranian people, a veiled effort to indicate to Tehran they do not want retaliation on American targets in the region.
“This mission was not and has not been about regime change,” Mr Hegseth added.
Mr Caine said the goal of the operation – destroying nuclear sites in Fordo, Natanz and Isfahan – had been achieved. US President Donald Trump earlier claimed the facilities had been “completely and fully obliterated”.
“Final battle damage will take some time, but initial battle damage assessments indicate that all three sites sustained extremely severe damage and destruction,” Mr Caine said.
The operation inserted the United States into Israel’s war aimed at destroying Iran’s nuclear programme, though the Atomic Energy Organisation of Iran insisted the programme will not be stopped.
Iranian President Masoud Pezeshkian has condemned the US attacks, while foreign minister Abbas Araghchi warned that diplomacy is no longer an option.
“This aggression showed that the United States is the primary instigator of the Zionist regime’s hostile actions against the Islamic Republic of Iran,” Mr Pezeshkian said on Sunday.
“Although they initially tried to deny their role, after our armed forces’ decisive and deterrent response and the Zionist regime’s clear incapacity, they were inevitably forced to enter the field themselves.”
Mr Araghchi meanwhile, declared that while the “door to diplomacy” should always be open, “this is not the case right now”.
He added: “The warmongering, lawless administration in Washington is solely and fully responsible for the dangerous consequences and far-reaching implications of its act of aggression.”
Satellite images taken on Sunday show damage to the mountainside at the underground site at Fordo.
The images, by Planet Labs PBC, show that the once-brown mountain now has parts turned grey and its contours appear slightly different than those in previous images, suggesting a blast threw up debris around the site.
That suggests the use of specialised American bunker-buster bombs on the facility. Light grey smoke also hung in the air.
Iran and the UN nuclear watchdog said there were no immediate signs of radioactive contamination at the three locations following the strikes.
It is not clear whether the US will continue attacking Iran alongside its ally Israel, which has been engaged in a nine-day war with Iran.
Mr Trump acted without congressional authorisation, and he warned that there will be additional strikes if Tehran retaliates against US forces.
“There will either be peace or there will be tragedy for Iran,” he said.
Iran’s foreign ministry said Washington had “betrayed diplomacy” with the military strikes, and that “the US has itself launched a dangerous war against Iran”.
Its statement added: “The Islamic Republic of Iran reserves its right to resist with full force against US military aggression and the crimes committed by this rogue regime, and to defend Iran’s security and national interests.”
Hours after the American attacks, Iran’s paramilitary Revolutionary Guard said it launched a barrage of 40 missiles at Israel, including its Khorramshahr-4, which can carry multiple warheads.
Israeli authorities reported that more than 80 people suffered mostly minor injuries, though one multi-storey building in Tel Aviv was significantly damaged, with its entire facade torn away to expose the apartments inside. Houses across the street were almost completely destroyed.
Following the Iranian barrage, Israel’s military said it had “swiftly neutralised” the Iranian missile launchers that had fired, and that it had begun a series of strikes towards military targets in western Iran.
Iran has maintained that its nuclear programme is for peaceful purposes only, and US intelligence agencies have assessed that Tehran is not actively pursuing a bomb. However, Mr Trump and Israeli leaders have argued Iran could quickly assemble a nuclear weapon, making it an imminent threat.
The decision to directly involve the US in the war comes after more than a week of strikes by Israel that significantly degraded Iran’s air defences and offensive missile capabilities, and damaged its nuclear enrichment facilities.
But US and Israeli officials have said American B-2 stealth bombers and the 30,000-pound bunker-buster bomb that only they have been configured to carry offered the best chance of destroying heavily fortified sites connected to the Iranian nuclear programme buried deep underground.
Mr Trump appears to have made the calculation – at the prodding of Israeli officials and many Republicans – that Israel’s operation had softened the ground and presented a perhaps unparalleled opportunity to set back Iran’s nuclear programme, perhaps permanently.
“We have completed our very successful attack on the three Nuclear sites in Iran, including Fordo, Natanz, and Esfahan,” Mr Trump said in a post on social media.
“All planes are now outside of Iran air space. A full payload of BOMBS was dropped on the primary site, Fordo. All planes are safely on their way home.”
Mr Trump later added: “This is an HISTORIC MOMENT FOR THE UNITED STATES OF AMERICA, ISRAEL, AND THE WORLD. IRAN MUST NOW AGREE TO END THIS WAR. THANK YOU!”
Israel announced on Sunday that it had closed its airspace to both inbound and outbound flights in the wake of the US attacks.
US officials said the attack used bunker-buster bombs on Iran’s Fordo nuclear fuel enrichment plant, while submarines launched about 30 Tomahawk missiles.
The decision to attack was a risky one for Mr Trump, who won the White House partially on the promise of keeping America out of costly foreign conflicts and scoffed at the value of American interventionism.
But he has vowed he will not allow Iran to obtain a nuclear weapon, and he had initially hoped the threat of force would bring the country’s leaders to give up their nuclear programme peacefully.
