“The biggest challenge, the biggest adversary we face at this point are the reckless, feckless and defeatist words of congressional Democrats and some Republicans,” the defense secretary declared in his prepared remarks to the House Armed Services Committee, before members had asked a single question.

The statement set a hostile tenor for the secretary’s first public testimony on Capitol Hill since the war began, coming after Republicans had for weeks refrained from exercising any public oversight of an operation undertaken without congressional authorization, and which polls indicate is unpopular.

At multiple points during the nearly five-hour hearing, Mr. Hegseth became so belligerent toward Democrats who questioned him that the Republican chairman of the committee halted the proceedings to urge the secretary to show respect to the lawmakers.

“Once I recognize a member, they have control of that five minutes,” the chairman, Representative Mike D. Rogers of Alabama, told Mr. Hegseth. “The witness has to recognize it’s their time.”

The tense session unfolded just before a 60-day milestone in the conflict that some in the G.O.P. have said could become a pivot point for their so far unconditional backing for President Trump’s conduct of the war, beyond which they may begin demanding more answers about objectives and a plan for extricating American troops.

“Here we are in a full-scale Mideast war, and we’ve seen the costs of that,” Representative Adam Smith of Washington, the senior Democrat on the panel, said, noting military and civilian casualties and asserting that “over a dozen countries now have been dragged into this war in one way or another.”

“Where is this going?” Mr. Smith asked.

Mr. Hegseth and Gen. Dan Caine, the chairman of the Joint Chiefs of Staff, provided few answers about an endgame, though their appearance did yield some new information about the costs and results of the military campaign.

The Pentagon comptroller, Jay Hurst, said the war had so far cost $25 billion, mostly because of the tens of thousands of bombs and missiles used, providing the first such official estimate since Mr. Trump began the operation. He did not elaborate on the figure, which was strikingly smaller than the $200 billion the Pentagon had initially requested for the conflict and suggested a major slowdown in expenditures since the start of the war, when officials estimated it had cost more than $11 billion in its first six days.

General Caine put the number of U.S. service members that had died during the war with Iran at 14, slightly above the Pentagon’s own tally of war casualties, which reflects 13 deaths.

After two months of war, General Caine testified, the Iranians “are weaker and less capable than they have been in decades.”

Still, when asked for a timetable or projected cost for finishing a mission that Mr. Trump initially said would be completed in “four to five weeks,” Mr. Hegseth demurred.

“As you know and as the president has stated, you would never tell your adversary, especially once you’ve decimated their military and you control their strait,” that information, he told Representative Chrissy Houlahan, Democrat of Pennsylvania.

Democrats sharply questioned the objectives for the mission and what had been gained from it. In one particularly heated exchange, Representative John Garamendi, Democrat of California, offered a tally of U.S. losses so far and asked what the United States had achieved, noting that Iran had retained significant military capabilities and closed the Strait of Hormuz, the strategic waterway for oil shipping.

“You have been lying to the American people since Day 1” of the war, Mr. Garamendi told Mr. Hegseth, accusing him of “incompetence.”

Mr. Hegseth responded by suggesting that the congressman was rooting for the enemy.

“I know the American people support that mission, despite your loose talk,” said Mr. Hegseth, who just a year ago put the flight sequencing of American fighter jets in a group chat on a commercial messaging app. Later, he asked Mr. Garamendi: “Who you cheering for here? Who you pulling for?”

In the hallway outside, protesters had gathered to register their opposition to the war, shouting “war criminal” and “arrest Hegseth” as he arrived to testify.

Many Republicans praised the war in Iran and Mr. Hegseth’s leadership, and focused their questions on issues such as quality of life improvements for service members, the use of artificial intelligence at the Pentagon and combating adversaries such as China.

But some in the G.O.P. made it clear they did not approve of Mr. Hegseth’s personnel decisions, including the recent firings of Navy Secretary John Phelan and of Gen. Randy George, the Army chief of staff.

“You have the constitutional right to do these things, but it doesn’t make it right or wise,” Representative Don Bacon, Republican of Nebraska, told Mr. Hegseth.

Later, Representative Austin Scott, Republican of Georgia, also criticized General George’s firing and appeared to beseech Mr. Hegseth not to alienate Democrats whose votes would be needed to secure military resources that some in the G.O.P. oppose.

“It takes 218 votes to get something across the floor of the House,” Mr. Scott said. “I just would encourage everybody to keep that in mind, because we’re going to lose some Republican votes.”

One point of agreement on the committee was the concern expressed over the nation’s dwindling weapons stockpile. Mr. Rogers warned that U.S. munitions stockpiles were dangerously low and that the nation’s industrial capacity to replenish them was weak. The war in Iran has sharply depleted U.S. arsenals, with the Pentagon diverting bombs, missiles and other hardware from commands in Asia and Europe to the Middle East.

But ultimately, Mr. Rogers said, the military campaign in Iran has given Mr. Trump “the opening he needs to negotiate a true and lasting peace that will ensure Iran never acquires a nuclear weapon.”

Still, even as the hearing unfolded, the conflict’s outcome was uncertain, with a fragile cease-fire and dueling blockades muddying the situation and no binding agreement yet on Iran’s nuclear program or significant change to the country’s leadership.

In a predawn social media post before the session began, Mr. Trump urged Iranian leaders to “get smart soon,” alongside an image of himself holding an automatic rifle in front of a hilly desert landscape dotted with explosions. He later told Axios that he was rejecting an Iranian proposal that sought to lift the naval blockade, saying he believed it was “somewhat more effective than the bombing.”

When asked by Representative Seth Moulton, Democrat of Massachusetts, how he would characterize the current state of the war, Mr. Hegseth called it “an astounding military success.”

“But are we winning the war?” Mr. Moulton asked.

“Absolutely,” Mr. Hegseth replied.

Eric Schmitt, Helene Cooper and John Ismay contributed reporting.