BEIRUT, Lebanon — Secretary of State John Kerry was clearly exasperated, not least at his own government.

Over and over again, he complained to a small group of Syrian civilians that his diplomacy had not been backed by a serious threat of military force, according to an audio recording of the meeting obtained by The New York Times.

“I think you’re looking at three people, four people in the administration who have all argued for use of force, and I lost the argument.”

The 40-minute discussion, on the sidelines of last week’s United Nations General Assembly in New York, provides a glimpse of Mr. Kerry’s frustration with his inability to end the Syrian crisis. He veered between voicing sympathy for the Syrians’ frustration with United States policy and trying to justify it.

The conversation took place days after a brief cease-fire he had spearheaded crumbled, and as his Russian counterpart rejected outright his new proposal to stop the bombing of Aleppo. Those setbacks were followed by days of crippling Russian and Syrian airstrikes in Aleppo that the World Health Organization said Wednesday had killed 338 people, including 100 children.

At the meeting last week, Mr. Kerry was trying to explain that the United States has no legal justification for attacking Mr. Assad’s government, whereas Russia was invited in by the government.

“The problem is the Russians don’t care about international law, and we do.”

Mr. Kerry has been hamstrung by Russia’s military operations in Syria and by his inability to persuade Washington to intervene more forcefully. He has also been unable to sell Syrian opponents of Mr. Assad, like the ones in that room, on a policy he does not wholeheartedly believe in.

His frustrations and dissent within the Obama administration have hardly been a secret, but in the recorded conversation, Mr. Kerry lamented being outmaneuvered by the Russians, expressed disagreement with some of Mr. Obama’s policy decisions and said Congress would never agree to use force.

“We’re trying to pursue the diplomacy, and I understand it’s frustrating. You have nobody more frustrated than we are.”

The meeting took place at the Dutch Mission to the United Nations on Sept. 22. There were perhaps 20 people around a table: representatives of four Syrian groups that provide education, rescue and medical services in rebel-held areas; diplomats from three or four countries; and Mr. Kerry’s chief of staff and special envoy for Syria. The recording was made by a non-Syrian attendee, and several other participants confirmed its authenticity.

John Kirby, a State Department spokesman, declined on Thursday evening to comment on what he described as a private conversation. He said that Mr. Kerry was “grateful for the chance to meet with this group of Syrians, to hear their concerns firsthand and to express our continued focus on ending this civil war.”

Several of the Syrian participants said afterward that they had left the meeting demoralized, convinced that no further help would come from the Obama administration. One, a civil engineer named Mustafa Alsyofi, said Mr. Kerry had effectively told the Syrian opposition, “You have to fight for us, but we will not fight for you.”

“How can this be accepted by anyone?” Mr. Alsyofi asked. “It’s unbelievable.”

In the meeting, he and the others pressed Mr. Kerry politely but relentlessly on what they saw as contradictions in American policy. Their comments crystallized the widespread sense of betrayal even among the Syrians most attractive to Washington as potential partners, civilians pushing for pluralistic democracy.

One woman, Marcell Shehwaro, demanded “the bottom line,” asking “how many Syrians” had to be killed to prompt serious action.

“What is the end of it? What he can do that would be the end of it?”

Mr. Kerry responded that “Assad’s indifference to anything” could push the administration to consider new options, adding, “There’s a different conversation taking place” since the intensified bombing of Aleppo and the further breakdown of talks with Russia.

But he also said any further American effort to arm rebels or join the fight could backfire.

“The problem is that, you know, you get, quote, enforcers in there and then everybody ups the ante, right? Russia puts in more, Iran puts in more; Hezbollah is there more and Nusra is more; and Saudi Arabia and Turkey put all their surrogate money in, and you all are destroyed.”

At another point, Mr. Kerry spelled out in stark terms distinctions the United States was making between combatants, which have upset the Syrian opposition: The United States wants the rebels to help it fight the Islamic State and Al Qaeda because, as he put it, “both have basically declared war on us.” But Washington will not join the same rebels in fighting Hezbollah, the Lebanese Shiite militia allied with Mr. Assad, even though the United States lists Hezbollah as a terrorist group like the others.

“Hezbollah,” Mr. Kerry explained, “is not plotting against us.”

He also spoke of the obstacles he faces back home: a Congress unwilling to authorize the use of force and a public tired of war.

“A lot of Americans don’t believe that we should be fighting and sending young Americans over to die in another country.”

One of the Syrians in the room assured Mr. Kerry, “No one is requesting an invasion,” but he insisted that the rebels needed more help.

As time ran short, Mr. Kerry told the Syrians that their best hope was a political solution to bring the opposition into a transitional government. Then, he said, “you can have an election and let the people of Syria decide: Who do they want?”

A State Department official, speaking on the condition of anonymity, said later that Mr. Kerry was not indicating a shift in the administration’s view of Mr. Assad, only reiterating a longstanding belief that he would be ousted in any fair election.

At one point, Mr. Kerry astonished the Syrians at the table when he suggested that they should participate in elections that include President Bashar al-Assad, five years after President Obama demanded that he step down.

Mr. Kerry described the election saying it would be set up by Western and regional powers, and the United Nations, “under the strictest standards.” He said that the millions of Syrians who have fled since the war began in 2011 would be able to participate.

“Everybody who’s registered as a refugee anywhere in the world can vote. Are they going to vote for Assad? Assad’s scared of this happening.”

But the Syrians were skeptical that people living under government rule inside Syria would feel safe casting ballots against Mr. Assad, even with international observers — or that Russia would agree to elections if it could not ensure the outcome. And that is when the conversation reached an impasse, with Ms. Shehwaro, an educator and social media activist, recalling hopes for a more direct American role.

“So you think the only solution is for somebody to come in and get rid of Assad?” Mr. Kerry asked.

“Yes,” Ms. Shehwaro said.

“Who’s that going to be?” he asked. “Who’s going to do that?”