In late April, Estonian authorities relocated a Soviet war memorial in the capital and exhumed the remains of soldiers buried there, sparking furious protest among ethnic Russians in the Baltic state, and in Russia.
"The Russian side made a firm request that Estonian authorities help relatives of the Soviet soldiers, whose remains were exhumed in Tallinn, in reburying them in line with their wishes," the Foreign Ministry's statement quoted Sergei Lavrov as saying.
At talks in Sweden with Estonian Foreign Minister Urmas Paet, Lavrov also urged an investigation into the death of a Russian national, Dmitry Ganin, who was stabbed during the protests in Estonia, where ethnic Russians make up about one-third of the population.
Earlier Wednesday, authorities in Tallinn said the remains of Captain Alexei Bryantsev, one of the 13 soldiers buried in the city in 1944, would be handed over to his son Viktor, who is now in the Estonian capital, pending a DNA test.
A Russian embassy spokesman said Viktor Bryantsev was expected to take the remains on a flight to Moscow Friday. Maxim Kozlov said Russia was covering all of Viktor's accommodation, DNA analysis and transportation costs.
Earlier reports said a ceremony to rebury the Red Army captain in his home town of Gukovo in southern Russia would take place Saturday.
The relatives of three other soldiers were earlier reported to have voiced plans to have their ancestors reburied in their homeland.
Estonian authorities said the remains of the soldiers - revered as heroes who helped defeat the Nazis, but regarded as occupiers by the Estonian leadership - who could not be identified would be reburied at a military cemetery in Tallinn on July 3.
Estonia's Defense Ministry said Russian relatives could ask for a new exhumation and reburial once they were laid to rest at the Estonian cemetery.