Lavrov in a statement called on Estonia to immediately launch an investigation into its police's response to riots sparked by the monument's removal last week from central Tallinn.
The riots left one Russian national dead and more than 150 people injured. The dead man was buried today and three activists involved in the disturbances were arrested by police.
There have been calls in Russia, from politicians and businesspeople, to boycott Estonian goods.
Russia's state railway monopoly halted deliveries of oil products to Estonia on May 2, saying it plans to carry out maintenance of the rail link to Estonia.
Lavrov also criticized the European Union for supporting Estonia, saying this contradicts European values.
The NATO military alliance and the United States have also pledged their support for Estonia.
Ethnic Russian Population
The monument at the heart of the dispute is seen by Russians as a memorial to Red Army soldiers who died fighting German Nazi troops. Many Estonians view it as a reminder of Soviet occupation.
Ethnic Russians make up about one-third of the Estonian population.
Protests are continuing outside the Estonian Embassy in Moscow to protest the monument's removal. The European Union has urged Moscow to honor its obligations under diplomatic treaties to protect the Estonian Embassy.
The embassy on May 2 suspended consular services after a deadline expired for the demonstrators to be removed.
The same day, some 40 activists from the pro-Kremlin youth groups Nashi and Young Russia stormed a news conference held by Estonian Ambassador to Russia Marina Kaljurand at the Moscow office of the newspaper "Argumenty i fakty."
Estonian President Toomas Hendrik Ilves has urged Russia to "remain civilized" in the spiraling dispute.
The country's prime minister, Andrus Ansip, has called on the European Union to help protect his country against "Russia's coordinated attacks."
(Compiled from agency reports)