The Soviet-era statue, depicting a Red Army soldier in uniform and dubbed the "Bronze Soldier," has been vandalized several times in recent years, and Laanet said it would now get round-the-clock police protection.
It has been a rallying point for several recent verbal battles between ethnic-Estonian and native Russian-speaking extremists. Police have been present at each and there has been no violence.
Red Army veterans and their supporters gather at the statue each year to lay flowers and commemorate the Soviet Union's role in the defeat of Nazi Germany.
But many Estonians are offended by these rallies, arguing that the Red Army may have helped liberate the country from the Nazis but it also helped enforce the nearly five decade-long totalitarian Soviet rule of the country.
Like Estonia, neighboring Latvia also has a large ethnic Russian minority. Most came to the countries during the Soviet occupation, which ended in 1991.
As a condition to get Russia to withdraw its troops from their countries in 1994, Estonia and Latvia agreed to maintain Red Army World War II monuments.
Laanet said Friday the government had not decided on the statue's future.
Estonian President Arnold Ruutel has suggested forming a commission to determine the monument's future. But Prime Minster Andrus Ansip rejected the idea, saying extremist groups would be given too much clout on such a panel.
After it turned out that Deputy Prime Minister Andrei Belousov included the Fonbet betting company in the list of backbone enterprises that can count on state support, everyone started talking about these bookmakers.