TALLINN, Estonia, May 24 — When Estonian authorities began removing a bronze statue of a World War II-era Soviet soldier from a park in this bustling Baltic seaport last month, they expected violent street protests by Estonians of Russian descent.

They also knew from experience that “if there are fights on the street, there are going to be fights on the Internet,” said Hillar Aarelaid, the director of Estonia’s Computer Emergency Response Team. After all, for people here the Internet is almost as vital as running water; it is used routinely to vote, file their taxes, and, with their cellphones, to shop or pay for parking.

What followed was what some here describe as the first war in cyberspace, a monthlong campaign that has forced Estonian authorities to defend their pint-size Baltic nation from a data flood that they say was set off by orders from Russia or ethnic Russian sources in retaliation for the removal of the statue.

The Estonians assert that an Internet address involved in the attacks belonged to an official who works in the administration of Russia’s president, Vladimir V. Putin.