Hegseth told politicians at a hearing in Washington the figure included certain aspects of the war as well as anticipated costs through September 30.
It was unclear how the Pentagon arrived at the $US37.5 billion figure. A source told Reuters in March that President Donald Trump's administration estimated the first six days of the war had cost at least $US11.3 billion.
Hegseth also told politicians that military training would need to be curtailed without an urgent funding boost.
This is the first time that Hegseth, who appeared before the Senate Appropriations Committee along with Chairman of the Joint Chiefs of Staff, General Dan Caine, has publicly faced questions from politicians since the US military restarted operations against Iran earlier this month.
With just six months before midterm elections in which Trump's Republicans may face an uphill battle to keep their House majority, Democrats are riding high in public opinion polls as they attempt to link the unpopular Iran war with affordability.
A fragile ceasefire between the United States and Iran collapsed earlier this month and both sides have been carrying out daily strikes against each other.
The number of US troops killed in the war on Iran rose to 17 over the weekend, while officials are examining the remains of another soldier missing following a strike on a base in Jordan. Two of the 17 were confirmed to have been killed when Iran attacked US personnel in Jordan.
Roughly 430 US troops have been injured so far in the conflict, which started in late February. The Pentagon said on Monday that 100 service members were injured since July 7, but that 96 per cent have returned to duty. It was unclear how many of those, if any, were included in the 430 number in the Pentagon's public database.
In the past week, Trump has threatened to expand the targets being struck in Iran to include energy plants and bridges, send ground forces to seize Iran's Kharg Island oil hub and bomb a deep-underground nuclear-linked site known as Pickaxe Mountain.
On Tuesday, Trump said the US would take out the mountain facility "pretty soon."
