Fighters opposed to the government in Moscow say they have captured some Russian soldiers in Belgorod, near the border with Ukraine.
Belgorod’s top official replied to say he had agreed to meet the men’s captors if the soldiers were still alive.
But later, the fighters said that the governor “had not found the courage” to meet them and they would hand over their captives to Ukraine.
Russia has blamed Ukraine for recent attacks in its border territories.
Kyiv denies being directly involved.
The Russian army said on Sunday its artillery had hit a “terrorist” group near the village of Novaya Tavolzhanka, adding that “the enemy scattered and retreated”.
Earlier, a group of paramilitaries issued a message on the Telegram app, saying they had captured two men but would hand them over if Belgorod governor Vyacheslav Gladkov agreed to talks.
The video purported to show both captives, although the BBC has been unable to independently verify their identities.
The message was posted by the Russian Volunteer Corps (RDK), and described as a joint statement with the Liberty of Russia Legion (FRL).
Mr Gladkov responded with his own Telegram video, saying he had agreed to the talks if the soldiers were shown to be still alive, adding that he thought they had probably been killed.
Later, the RDK posted a further video – this time appearing to show more captives, in which they said that Mr Gladkov had failed to turn up for the meeting.
They said they would now hand over the captives to Ukraine, to be subject to an exchange with Ukrainian prisoners of war.
Both the RDK and the FRL want to topple President Vladimir Putin, and also oppose the full-scale invasion of Ukraine that he launched in February last year.
Ukrainian officials say the two paramilitary organisations consist of Russian citizens who want to create a “security zone” for Ukrainians.
The RDK came to prominence in March for a cross-border raid in Russia’s Bryansk region. Its leader is a Russian nationalist with alleged links to neo-Nazis.
The FRL is considered a different sort of organisation that fights alongside Ukrainian troops against Russian forces.
In his video, Mr Gladkov labelled the fighters in question “scoundrels, murderers, fascists”, but promised to “guarantee safety” if the talks took place.
And though they asked him to go to Novaya Tavolzhanka to meet them, he said this was too dangerous and that he would expect them at a checkpoint in the town of Shebekino.
Mr Gladkov has not commented on the events since the video, but posted pictures of a meeting with regional and federal officials.
There has been a spate of attacks in Belgorod recently – notably including a major cross-border incursion late last month which Moscow said ended in the deaths of 70 insurgents.
Kyiv has denied having any direct involvement in such attacks.
But it has painted the growing violence in Russian territory as being the inevitable consequence of Russia’s invasion last year.