CHISINAU, Moldova – Vova Klever, a young, successful fashion photographer from Ukraine’s capital, Kyiv, did not see himself in this war.

“Violence is not my weapon,” he said.

So shortly after Russia invaded Ukraine in late February, Mr. Klever sneaked out, breaking the Ukrainian law that prohibits men of military age from leaving the country.

Mr. Klever’s mistake, which would bring devastating consequences, was writing to a friend about being smuggled out and making it to London.

The friend betrayed his trust and posted their conversation on social media. It went viral, and Ukrainians all over the internet exploded with anger and resentment.

“You are a walking dead person,” one Twitter message said. “I’m going to find you in any corner in the world.”

The notion of people — especially men — leaving war-torn Ukraine for safe and comfortable lives abroad has provoked a moral dilemma among Ukrainians that turns on one of the most elemental decisions humans can make: fight or flee.

Thousands of Ukrainian men of military age have left the country to avoid participating in the war, according to records from regional law enforcement officials and interviews with people inside and outside Ukraine. Smuggling rings in Moldova, and possibly other European countries, have been doing a brisk business. Some people have paid up to $15,000 for a secret night-time ride out of Ukraine, Moldovan officials said.

The draft dodgers are the vast exception. That makes it all the more complicated for them — morally, socially and practically. Ukrainian society has been mobilized for war against a much bigger enemy, and countless Ukrainians without military experience have volunteered for the fight. To maximize its forces, the Ukrainian government has taken the extreme step of prohibiting men 18 to 60 from leaving, with few exceptions.

All this has forced the Ukrainian men who don’t want to serve into taking illegal routes into Hungary, Moldova and Poland and other neighboring countries. Even among those convinced they fled for the right reasons, some said they felt guilty and ashamed.

“I don’t think I can be a good soldier right now in this war,” said a Ukrainian computer programmer named Volodymyr, who left shortly after the war began and did not want to disclose his last name, fearing repercussions for avoiding military service.

“Look at me,” Volodymyr said, as he sat in a pub in Warsaw drinking a beer. “I wear glasses. I am 46. I don’t look like a classic fighter, some Rambo who can fight Russian troops.”

He took another sip and stared into his glass.

“Yes, I am ashamed,” he said. “I ran away from this war, and it is probably my crime.”

Ukrainian politicians have threatened to put draft dodgers in prison and confiscate their homes. But within Ukrainian society, the sentiments are more divided.

The vast majority of refugees are women and children, who have faced little backlash. But that’s not the case for young men. As cities continue to be pummeled by Russian bombs, many Ukrainians have been unsparing toward the draft dodgers.

This is what blew up on the young photographer.

In mid-March Olga Lepina, who has worked as a model and a modeling agent, said Mr. Klever sent her husband a message saying he had made it to London.

Her husband wrote back: “Wow! How?”

“Through Hungary with the smugglers for 5k $,” Mr. Klever replied, according to screenshots of the conversation provided by Ms. Lepina. “But that’s just between us, shush!”

Ms. Lepina said she and Mr. Klever had been friends for years. She even went to his wedding. She had left, too, for France, with her husband, who is not a Ukrainian citizen. But as the war drew near, she said, Mr. Klever became intensely patriotic and a bit of an online bully. When she found out he had avoided service, she was so outraged that she posted screenshots of the conversation on Instagram.

“For me, it was a hypocrisy to leave the country and pay money for this,” she explained. “I just decided to bring it to the public. He needs to be responsible for his words.”

Mr. Klever, who is in his 20s, was bombarded with hate-filled messages, including death threats. Some Ukrainians resented that he used his wealth to get out and called it “cheating.”

Responding to emailed questions, Mr. Klever did not deny skipping out on his service and said that he had poor eyesight and had “been through a lot lately.”

“You can’t even imagine the hatred,” he said.

Mr. Klever gave conflicting accounts of how exactly he exited the country and declined to provide details. But for many other Ukrainian men, Moldova has become the favorite trap door.

Moldova shares a nearly 800-mile border with western Ukraine. And unlike Hungary, Poland, Romania and Slovakia, Moldova is not part of the European Union, which means it has significantly fewer resources to control its frontiers. It is one of Europe’s poorest countries and has been a hub of human trafficking and organized crime.

Within days of the war erupting, Moldovan officials said, Moldovan gangs posted advertisements on Telegram, a popular messaging service in Eastern Europe, offering to arrange cars, even minibuses, to spirit out draft dodgers.

Law enforcement officials said the typical method was for the smugglers and the Ukrainians to select a rendezvous point along Moldova’s “green border,” the term used for the unfenced border areas, and meet late at night.

On a recent night, a squad of Moldovan border guards trudged across a flat, endless wheat field, their boots sinking in the mud, looking for draft dodgers. There was no border post, just the faint lights of a Ukrainian village and the sounds of dogs barking in the darkness.

Out here, one can just walk into and out of Ukraine.

Moldovan officials said that since late February they had broken up more than 20 smuggling rings, including a few well-known criminal enterprises. In turn, they have apprehended 1,091 people crossing the border illegally. All were Ukrainian men, officials said.

Once caught, these men have a choice. If they don’t want to be sent back, they can apply for asylum in Moldova, and cannot be deported.

But if they do not apply for asylum, they can be turned over to the Ukrainian authorities, who, Moldovan officials said, have been pressuring them to send the men back. The vast majority of those who entered illegally, around 1,000, have sought asylum, and fewer than 100 have been returned, Moldovan officials said. Two thousand other Ukrainian men who have entered Moldova legally have also applied for asylum.

Volodymyr Danuliv is one of them. He refuses to fight in the war, though it’s not the prospect of dying that worries him, he said. It is the killing.

“I can’t shoot Russian people,” said Mr. Danuliv, 50.

He explained that his siblings had married Russians and that two of his nephews were serving in the Russian Army — in Ukraine.

“How can I fight in this war?” he asked. “I might kill my own family.”

Myroslav Hai, an official with Ukraine’s military reserve, conceded, “There are people who evade mobilization, but their share in comparison with volunteers is not so large.” Other Ukrainian officials said men ideologically or religiously opposed to war could serve in another way, for example as cooks or drivers.

But none of the more than a dozen men interviewed for this article seemed interested. Mr. Danuliv, a businessman from western Ukraine, said he wanted no part in the war. When asked if he feared being ostracized or shamed, he shook his head.

“I didn’t kill anyone. That’s what’s important to me,” he said. “I don’t care what people say.”

What happens when the war ends? How much resentment will surface toward those who left? These are questions Ukrainians, men and women, are beginning to ask.

When Ms. Lepina shamed Mr. Klever, she was no longer in Ukraine herself. She had left, too, for France. Every day, she said, she wrestles with guilt.

“People are suffering in Ukraine, and I want to be there to help them, to support them,” she said. “But at the same time I’m safe and I want to be here.”

“It’s a very ambiguous, complicated feeling,” she said.

And she knows she will be judged.

“Of course there will be some people who divide Ukrainian nationals between those who left and those who stayed,” she said. “I am ready for that.”

Siergiej Greczuszkin contributed reporting from Warsaw, and Daria Mychkovska from Przemysl, Poland.