The government was hoping the gesture would begin a process of reconciliation between ethnic Estonians and Russian-speakers, 10 days after Estonia was hit by riots over the decision to move the statue from downtown Tallinn to a cemetery outside the city center.
The Swedish ambassador to Estonia, Dag Hartelius, laid a wreath on behalf of the Western diplomatic corps. Russian Ambassador Nikolai Uspensky refused to take part in the ceremony.
Russia was furious at Estonia's decision to move the statue and a nearby war grave from downtown Tallinn. On Monday Foreign Minister Sergey Lavrov, lashed out at the European Union and NATO for doing nothing to stop the monument's relocation.
Estonia's ethnic Russians - who make up about one-fourth of the country's population of 1.3 million - took their frustration to the streets, resulting in the worst rioting Estonia has seen since it broke from the Soviet Union in 1991.
For Russia, the Bronze Soldier symbolizes the enormous human sacrifice the Soviet Union paid in defeating Nazi Germany, while Estonians are reminded of 50 years of Soviet occupation and totalitarian rule.
Earlier on Tuesday Estonian ministers and chief rabbi of Estonia's Jewish community, Shmuel Kot, laid flowers at the former Klooga concentration camp 40 kilometers (25 miles) west of Tallinn.
The discovery of the submarine has unveiled a few "inconsistencies." For example, how can one explain the fact that the sub was found where it needed to be searched for from the start?
When on a state visit to Singapore, Russian President Vladimir Putin promised to revisit the discussion of the 1956 Declaration between the USSR and Japan regarding the issue of the peace treaty with Japan
The TurkStream, which runs along the bottom of the Black Sea from Russia's Anapa to Turkey, will consist of two lines, each with a capacity of 15.75 billion cubic meters of gas a year