Despite a temporary ban on public gatherings imposed after the clashes, a few hundred people showed up at the square, but no incidents were reported.
Hundreds of people also gathered to lay flowers at the statue's new location, a military cemetery outside the city centre.
The Bronze Soldier commemorates Red Army troops killed fighting the Nazis, but many Estonians consider it a bitter reminder of the five decades of foreign occupation that followed the Soviet victory.
Russia's ambassador to Estonia laid a wreath at the statue, while reiterating Moscow's objections to the relocation of both the monument and a nearby war grave containing 12 Red Army soldiers.
"If we are to speak bluntly they [Estonia] have desecrated the graves," Nikolai Uspensky said.
"Of course we look upon this negatively, and it creates the lowest of feelings."
In Latvia, a massive police presence prevented a clash between ethnic Russians, who make up one-third of the country's 2.3 million population, and a small group of radical Latvian nationalists, who laid flowers with black ribbons at the Soviet victory monument.
In Lithuania, war veterans and ambassadors from Russia, Ukraine, Belarus and other former Soviet republics gathered at the Soviet memorial in Vilnius' Antakalnis cemetery.
Commenting the recent events in Estonia, Vladimir Drazin, the Belarusian ambassador said, "It's painful to see that someone is trying to spark a conflict between European nations, but I believe that fascism will never rise again."