KROPYVNYTSKIY, Ukraine—The Russian soldiers who showed up at Rev. Sergey Chudinovich’s church put a bag over his head, took him to the police station, then made him an offer.

Let us distribute aid at your church, they said, which is located in Russian-occupied Kherson in the south of Ukraine. Or make a video telling residents to accept Russian aid.

Fr. Chudinovich refused. The Russians tied him up, tossed him in the basement and tortured him for the next two days, he said.

In Russian-occupied parts of Ukraine, clergy members are targets.

Dozens of priests from the Orthodox Church of Ukraine, the country’s largest denomination, have been kidnapped or killed since the invasion began, according to church officials. Still more pastors from other denominations have been chased from their pulpits and imprisoned. Some have had their church property seized. One priest trying to leave occupied territory was asked whether he knew several other clergy members in the region. 

The Russians have accused detained clergy of organizing protests, working as U.S. agents or aiding the Ukrainian military. But as Moscow worked to consolidate its hold on occupied territory, priests say it was their influence within the local population that made them targets for Russians to try to turn to their side—or eliminate.

“They’ve tried to find those who have power and authority among the local people—who are able to be leaders of resistance,” said Archbishop Evstratiy of Chernihiv, a spokesman for the Orthodox Church of Ukraine. “Clergy of the Ukrainian church, unfortunately, are in the first row.”

Fr. Chudinovich shows a video he said was taken when he buried Ukrainian soldiers killed in Kherson in the early days of Russia’s invasion.

Russia has made religion a central pillar of its war effort. Patriarch Kirill, leader of the Russian Orthodox Church, has called the war a metaphysical conflict between the faithful of God and a decadent West. Both he and Russian President Vladimir Putin have assailed the establishment of the autonomous Orthodox Church of Ukraine in 2019 as a devious Western scheme to divide the two countries. The new church quickly overtook the local arm of the Russian Orthodox Church as the most popular.

Archbishop Evstratiy said the hunt for Ukrainian Orthodox priests began in the first days of the war.

In the Kyiv suburb of Bucha, he said, neighbors of one priest said Russians showed up at his house asking for him the same day they arrived in town. The priest had already fled, Archbishop Evstratiy said, but another priest in the town was killed at a checkpoint.

In Ivankiv, north of Kyiv, a priest wearing his cassock was pulled out of his car and shot at a checkpoint where his body lay for several days, Ukrainian Orthodox officials said.

In Bohdanivka, a village east of the capital, Russian troops put bullet holes through a cross along the main road, and broke another cross inside Rev. Antoniy Pyasetskiy’s Orthodox church. Fr. Pyasetskiy, who fought in the Soviet army in Afghanistan, said he and another priest were detained while checking on a local resident. The soldiers told them to strip and searched them for tattoos in the street, beat them and forced them to walk two hours to a Russian base.

When allowed to leave later that day, Fr. Pyasetskiy said he had several teeth missing. The other priest, who had been beaten so severely that Fr. Pyasetskiy said his face was unrecognizable, had to walk home naked.

“They kept saying, ‘Where is your God? Why isn’t he helping you,’” Fr. Pyasetskiy said of the soldiers. “It was just a show of disrespect to damage the cross.”

Fr. Chudinovich re-enacting his detention by Russians in the basement of his church in Kherson.

Ukrainian clergy from other denominations have also run afoul of Russian forces—particularly in the south, which has now been occupied for five months. Many of their encounters with the Russians began with an alleged transgression and ended with demands to collaborate.

Viktor Sergeev, the pastor of a Pentecostal Baptist church in Melitopol, said dozens of soldiers woke him around 5 a.m. one day in early March and pulled him, his adult sons and some neighbors from their homes.

The soldiers battered their way into the church where they interrogated them and smashed the windows. They asked whether the men had helped organize anti-Russian protests and where they got money for the church—a large building with a recording studio and a gymnasium—and insisted they must be getting funding from foreigners.

“The Russians said, ‘You’re an American sect. You train partisans here. Sects like yours are illegal in Russia,’” Mr. Sergeev said.

Mr. Sergeev told them he had only held prayer vigils for peace at his church, but they had more demands. They asked him to make a video in front of the church chanting “Russia, Russia,” plus another video criticizing the Ukrainian government. They also asked for a list of businessmen who came to the church. Mr. Sergeev said he would.

“The Russians realize we can influence people—that we’re opinion leaders in the city,” said Mr. Sergeev, whose church had 1,500 members before the war. “They were looking for us to collaborate.”

Two days later, the mayor of Melitopol, a southern port city in the Zaporizhzhia region, was detained by Russians. The Sergeev family fled to Ukrainian-held territory the next day, without recording a video.

In late July, a group of Russians showed up at the church and told the people there that it was illegal and that the building was being seized, Mr. Sergeev said.

Fr. Chudinovich has continued to send humanitarian aid to Russian-occupied Kherson.

In the first month of the war, Fr. Chudinovich turned his Kherson church into a local aid center, where he and his members offered haircuts, medicine and food. A sign on the wall advertised two-tiered coffee prices: 1,000 hryvnia, equivalent to about $27, if you ordered in Russian, no charge if you spoke Ukrainian. A photo of the sign wound up on social media in late March. The Russians showed up at the church the next morning.

After Fr. Chudinovich declined to let them distribute aid at his church, he said, they found some numbers of Ukrainian soldiers and policemen in his phone. They blindfolded him, he said, and took him to the basement.

Over the next two days, Fr. Chudinovich said, the Russians grilled him about his acquaintances. They left him in the cold without shoes, beat him in the knees and chest with a police baton, choked him until he passed out, and taunted him, saying: “Your God doesn’t exist.” At one point, he said, they tried to rape him with a stick.

On March 30, they released him after forcing him to make two videos, in which he said he was treated well by the Russians, and he pledged to make another one once home and post it on social media.

He did so, then fled to Ukrainian territory, where his family had been since the start of the war. A few weeks later, he posted another video to Facebook, detailing what had really happened to him in Russian captivity.

Fr. Chudinovich said he has tried to continue his work sending humanitarian aid to Kherson. But the videos have shaken associates’ trust in him—a common reaction after locals in the south are picked up by Russians. He now struggles to raise money for his church and his family.

“I have no job. I had partners in Mykolaiv who I used to work with to get medicine. After the interrogation, 80% of them stopped working with me,” he said. “I understand. Once someone is picked up, who knows what they will say.”

Marta Sydoryak and Nikita Nikolaienko contributed to this article.

Fr. Chudinovich said the videos he was forced to make shook his associates’ trust in him, and he now struggles to raise money.