Hurst said most of the expenses had been for munitions and to replace equipment.
Hurst told the lawmakers that a full assessment of the cost will be provided at a later time. The US and Iran have agreed on a ceasefire to allow for peace talks, but the conflict has not officially ended.
Money was a major talking point during the hearing.
The White House has asked Congress to boost the US defence budget to $1.5tn (£1.1tn), a sweeping rise that would mark the largest expansion in military spending since World War Two.
Hegseth told the committee the budget request “reflects the urgency of the moment”.
Gen Caine said the $1.5tn “represents a historic down payment for future security” that would allow the US to get ahead of fast-evolving technology.
Democrats on the committee often characterised the US military action in Iran as an expensive “war of choice” waged without the approval of Congress.
“You have been lying to the American public about this war from day one, and so has the president,” California Democrat John Garamendi said. He told Hegseth that Trump was “stuck in a quagmire” of another war in the Middle East.
Hegseth called Garamendi’s statement “reckless”, and denied Trump was in a “quagmire”. “Your hatred for President Trump blinds you,” Hegseth said.
Many Republicans on the committee were largely supportive of the Pentagon, with congressman Carlos Gimenez of Florida saying he believes Iran is an existential threat to the US.
“When someone tells me for 47 years that they want to kills us, I think I am going to take them at their word,” he said. “I support our efforts to make sure that Iran never has a nuclear weapon.”
The often-combative hearing also discussed the international economic ramifications of the war such as the rise in global oil prices, and its knock-on impacts for the price of other goods.
At one point, Hegseth hit back with a defiant tone, telling a congressman “shame on you”.