"We have more and more options, and they have less ... in only one month we set the terms, the upcoming days will be decisive," Hegseth said.
"Iran knows that, and there's almost nothing they can militarily do about it."
Hegseth, citing intelligence, said the strikes were damaging the morale of the Iranian military.
This, he said, was triggering widespread desertions, key personnel shortages and causing frustration amongst senior leaders.
Talks aimed at ending the conflict were ongoing and gaining strength, Hegseth added.
Hegseth also said he had visited troops in the Middle East on Saturday to witness the military operation against Iran.
Earlier on Tuesday, US President Donald Trump urged countries that did not help in the US-Israeli strikes on Iran to buy oil from the United States and go to the Strait of Hormuz and "just TAKE it".
Trump singled out the United Kingdom and France as unhelpful in the month-long war that has roiled global markets, driven up energy prices and allowed Iran to mostly close oil tanker traffic through the Strait.
"All of those countries that can't get jet fuel because of the Strait of Hormuz, like the United Kingdom, which refused to get involved in the decapitation of Iran, I have a suggestion for you: Number 1, buy from the US, we have plenty, and Number 2, build up some delayed courage, go to the Strait, and just TAKE IT," Trump said in a Truth Social post.
"You'll have to start learning how to fight for yourself, the USA won't be there to help you anymore, just like you weren't there for us.
"The hard part is done. Go get your own oil!"
He also criticised France for not letting planes carrying military supplies to Israel fly over French territory.
Trump's social media post came after US strikes hit a city that is home to one of Iran's main nuclear sites, sending a massive fireball into the sky, and Iran attacked a fully loaded Kuwaiti oil tanker in the Persian Gulf.
More vessels were flowing through the Strait of Hormuz, Hegseth told the briefing.
"There are countries around the world who ought to be prepared to step up on this critical waterway as well," he told reporters.
with AP
