Toomas Hendrik Ilves said: "All this had nothing to do with the inviolability of graves or keeping alive the memory of men fallen in World War II."
Quiet has returned to the streets of Tallinn after overnight clashes, looting and vandalism sparked by the government's move to relocate the Bronze Soldier - a monument to Red Army soldiers killed fighting the Nazis.
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 Red Army 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.