Two-and-a-half years into the war, with tens of thousands dead and Russia advancing in the east, some Ukrainians are asking a question that had until recently been taboo: Is it time to try to negotiate?

Opinion polls show that support for some kind of negotiations with Moscow has been creeping upward since Ukraine’s counteroffensive last year failed to retake significant territory—though a majority of Ukrainians still say they want to keep fighting to retake all Russian-occupied land. Ukrainian President Volodymyr Zelensky said he hopes to use the territory Kyiv has seized in Russia’s Kursk region as leverage for a peace deal.

But one key group remains particularly skeptical about any deal with Russia: the military. One recent survey found that 18% of veterans and active-duty members of the military believed Ukraine should seek to end the war through negotiations, the lowest of any demographic group in the study. Fifteen percent of soldiers and veterans said they would join an armed protest if Kyiv signed a peace treaty that they didn’t agree with.

“There’s war fatigue in Western society, and certainly in Ukrainian society,” said Col. Andriy Biletskiy , the commander of one of Ukraine’s largest brigades. “This is not the most optimistic moment for Ukraine, but no military catastrophe has occurred. This war is not lost.”

In an interview with The Wall Street Journal, Biletskiy said it wasn’t his place to weigh in on what an appropriate peace settlement would be, which he called a political question. But he said he decided to speak publicly—something he has rarely done since the start of the invasion in February 2022—in response to the shifting national mood, which he said was hurting the motivation of troops at the front.

The 45-year-old is a polarizing figure, a former commander of the volunteer Azov Battalion, some of whose members have espoused ultraright ideologies and used symbols including swastikas. Biletskiy, who calls himself a conservative, denies ever having any Nazi ideas or affiliations. The U.S. recently lifted a ban on military aid to the unit.

In Ukraine, Biletskiy is also influential, especially within the military: a former member of parliament and founder of the 3rd Assault Brigade, which is among Ukraine’s most highly regarded military units.

From a military perspective, he said, Ukraine didn’t need to seek a cease-fire. Though Kyiv has suffered some defeats over the past year, he called them relatively minor, adding that Russia still had many problems of its own: A poorly trained fighting force and lack of lower-level officers has meant that most of its advances—like the capture of the eastern city of Avdiivka earlier this year—come with massive casualties.

“Ukraine can recapture at least a very significant part of the territories,” he said. “I see a huge danger in stopping the war at random.”

Last week, Russian President Vladimir Putin said he was open to peace talks, but only on terms that Ukraine has previously dismissed as unworkable.

In interviews, troops and veterans—many of whom have been fighting since Russia first covertly invaded eastern Ukraine in 2014—expressed skepticism about pausing the conflict. Many were convinced that Putin would only use a break in combat to retool Russia’s military, then invade again. Others said the sacrifice of fallen comrades would have been in vain if Ukraine simply agreed to surrender territory to Russia.

Ivan Panchenko , a 42-year-old veteran who began fighting in 2014 and was discharged following a battlefield injury last year, said he would oppose any plan that surrendered Ukrainian territory.

“Russia has violated dozens of international treaties over the past 30 years—an agreement with them is worthless,” he said. “If we want a peace that will last a long time, we need to hurt them as much as possible.”

Though polls show that the general public also remains skeptical of deals with Putin, many—especially younger people—are ready to accept an imperfect peace to stop the war.

Alla Pronina , a 33-year-old schoolteacher in the southeastern city of Zaporizhzhia, said she began to reconsider the possibility of negotiations after last year’s counteroffensive. Now, with her husband away fighting, she is willing to give up all the territory Russia currently occupies in exchange for peace.

“Where can we go with this war?” she said.

Officially, such statements remain taboo. After a Russian missile struck a children’s hospital in Kyiv last month, Nastya Umka , a popular Kyiv blogger, posted to her roughly 600,000 followers on Instagram that there was no need to restore Ukraine’s 1991 borders and blamed politicians for the protracted conflict. “People want peace,” she wrote. Soon after, Umka said, Ukraine’s domestic intelligence agency, the SBU, called her in to speak. Umka declined to comment on what happened.

Still, Volodymyr Dubovyk , director of the Center for International Studies in Odesa, Ukraine, said the shifting public opinion has given Zelensky an opportunity to forge some kind of deal.

“The very fact that people appear to be more ready to have negotiations with Russia is a big change,” Dubovyk said. But he added that any cease-fire came with significant political risk: “It would probably be seen by a lot of Ukrainians as a bad deal.”

Yet, continuing the war presents its own political challenges for Zelensky.

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A handout photo made available by the National Police of Ukraine press service shows rescuers working at the site of a combined Russian strike that hit a residential area in Lviv, western Ukraine, 04 September 2024, amid the ongoing Russian invasion. At least seven people died, including three children, and 35 others were injured as a result of a Russian combined attack by shock drones and rockets of different types in Lviv, according to Lviv Mayor Andriy Sadovy. Russian troops entered Ukrainian territory on 24 February 2022, starting a conflict that has provoked destruction and a humanitarian crisis. EPA/NATIONAL POLICE OF UKRAINE

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A Ukrainian serviceman embraces an injured man at the site of residential buildings damaged during a Russian drone and missile strike, amid Russia’s attack on Ukraine, in Lviv, Ukraine September 4, 2024. REUTERS/Roman Baluk

Ukrainian brigades on the eastern front are desperately short of men and weaponry . Continued support from the U.S. might depend on the results of the election in November.

Earlier this year, Zelensky’s government lowered the age of conscription from 27 to 25 in an effort to address the manpower shortage. However, many of those who are being drafted are older, less fit and less motivated than those who volunteered at the outset of the war, according to military commanders.

One 37-year-old soldier fighting in the east said men who had just arrived in his unit from a training center were deployed to trenches the next day, where he expected them to take heavy casualties because of the lack of experience. “We’re still following the Soviet instructions on the training ground—not paying attention to the things you really need in war, like medical training,” the soldier said.

Many soldiers fighting in the east say a divide has opened between those who are fighting and those in the country’s major cities, who pay little attention to the war, like in the years from 2016 to 2022, when the front line was nearly frozen. In Dnipro, just a few hours from the eastern front, bars and cafes are full of young men sipping coffees or beers, as though there were no war.

“I don’t understand why society pretends nothing is happening,” said one 45-year-old major fighting in the east. “The government has created circumstances where those who are really motivated won’t accept agreements that give territory away. But those who aren’t fighting will make decisions. It’s painful.”

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Biletskiy said it is natural for those not fighting to live normally. “We cannot dress a nation of 37 million people in green and send them to the front,” he said. “We cannot stop life.”

Still, he said that many of the Ukrainian military’s problems could be addressed by improving training for new recruits. His own brigade, he said, has no issues with manpower shortages, because it is known as a unit where troops will receive proper training before they are sent to the trenches.

“When a person is poorly trained—when he does not know what will happen in the war, how he will perform his task, save his life or his comrade-in-arms—then he is afraid, and this is normal,” Biletskiy said. “A trained soldier is much less afraid.”

Write to Ian Lovett at ian.lovett@wsj.com