MOSCOW, May 18 — The computer attacks, apparently originating in Russia, first hit the Web site of Estonia’s prime minister on April 27, the day the country was mired in protest and violence. The president’s site went down, too, and soon so did those of several departments in a wired country that touts its paperless government and likes to call itself E-stonia.

Then the attacks, coming in waves, began to strike newspapers and television stations, then schools and finally banks, raising fears that what was initially a nuisance could have economic consequences.

The attacks have peaked and tapered off since then, but they have not ended, prompting officials there to declare Estonia the first country to fall victim to a virtual war.

“If you have a missile attack against, let’s say, an airport, it is an act of war,” a spokesman for the Estonian Defense Ministry, Madis Mikko, said Friday in a telephone interview. “If the same result is caused by computers, then how else do you describe that kind of attack?”