The Russian embassy to Lithuania described the decision as disgusting and undermining historical memory.
"This is a disgusting decision that insults the memory of 970 soldiers, including the four Soviet heroes who died in 1944 while liberating this territory of Lithuania from fascist German invaders," it said in a statement.
The embassy said that the decision by Biržai officials would be assessed by lawyers.
The first explanatory sign has been put up at a Soviet-era cemetery in Nemunėlio Radviliškis, with plans to place such signs next to monuments to Soviet soldiers in Biržai itself and in Vabalninkas, another small town in the district.
The daily Lietuvos Žinios reported last week that politicians in Biržai had long thought about how put up explanations at such places about the Soviet Union's contribution to World War II and its subsequent occupation of Lithuania.
Biržai Vice-Mayor Irutė Varžienė says that the upcoming centenary of the restoration of Lithuania's statehood added urgency to solving the problem.
"I think that these signs do not undermine historical truth. What they do is explain in a precise historical manner that these inscriptions that glorify Soviet soldiers and thank them do not reflect historical truth," she told BNS.
Dalius Mikelionis, an officer in charge of heritage at the town, said, "I'm not sure they were actually liberators, given that our people had to fight against them in the forests for ten years after that and that they did not return from these forests".
Active guerrilla fighting for Lithuania's independence took place between 1944 and 1953, claiming the lives of over 20,000 participants of the resistance efforts, their family members and supporters.
Some 275,000 people were sent to forced labor camps and deported from Lithuania during the Soviet occupation.