Toomas Hendrik Ilves, the president, said: "All this had nothing to do with the inviolability of graves or keeping alive the memory of men fallen in World War II."
The government of Estonia removed the Bronze Soldier - a monument to Soviet soldiers - from its prominent position in Tallinn, the capital, on Friday morning, promising to re-erect it in another location.
The decision sparked fierce rioting from Estonia's ethnic Russian minority on Thursday night and again on Friday, after the monument was removed secretly before dawn.
On Friday evening, fresh clashes broke out between riot police and bottle-wielding protesters but by midnight most demonstrators had left the streets.
One man was stabbed to death and dozens were injured - including 12 police officers - in the worst riots Estonia has seen since regaining independence from the Soviet Union in 1991, Martin Jasko, a government spokesman, said.
Some 300 people were detained.
The clashes started late on Thursday after a day of mostly peaceful protests against the plans to move the statue and exhume the remains of Soviet soldiers buried nearby.
Estonia's Russian speakers - roughly one-third of the country's 1.3 million population - see the monument as a tribute to Soviet soldiers who died fighting Nazi Germany.
Many ethnic Estonians, however, consider the memorial a painful reminder of the hardships they endured during five decades of Soviet rule, and wanted it removed from the city centre.