The popular Gazeta.Ru website said several dozen soldiers would be prosecuted after fleeing a training ground in southern Russia where they were under pressure to "volunteer" to fight in Ukraine.
The troops had freely enlisted for the army and are not draftees, it said.
It is the latest report to allege Russian soldiers are being sent to eastern Ukraine despite Moscow's insistence only "volunteers" are fighting alongside the pro-Russian separatists.
The defence ministry said the soldiers are under investigation for "disciplinary offences", the Echo of Moscow radio station reported.
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A lawyer representing five of the soldiers, Tatiana Chernetskaya, speaking by phone to AFP confirmed the report and said "dozens" of soldiers faced tribunals.
"They all have the same story. They all served together in the same unit," said Chernetskaya, based in the southern town of Krasnodar.
"They weren't directly forced to go to Ukraine. People came to the unit to canvass them to go," Chernetskaya said, adding the recruiters were "not wearing any identification tags."
The soldiers fled, not wanting "to find themselves in battle," she said.
Since Russia is technically not at war with Ukraine, "if they were sent to Ukraine, it could be seen as a criminal act," she added.
"They went back to Maikop and started writing resignation statements but these were not accepted and this all led to the launching of criminal cases."
She said soldiers started going on trial in March and several had already been convicted.