The Estonian government has said that its state and commercial websites, including a number of banks, are being bombarded by mass requests for information which are overwhelming their computer servers. Other targets of the "denial-of-service attacks" have included the Estonian foreign and defense ministries and leading newspapers and banks.
Officials have cut access to some servers from outside Estonia to prevent them from being attacked.
Estonian authorities said the attacks began after a Soviet war memorial in Tallinn was removed, an action that was condemned by the Kremlin.
Many of the attacks have come from Russia and are being hosted by Russian state computer servers, according to Tallinn officials. Moscow has denied any involvement.
A NATO spokesman said the organization was giving Estonia technical help.
"In the 21st century it's not just about tanks and artillery," NATO spokesman James Appathurai told BBC News. "We have sent one of our experts at the request of the Estonian authorities to help them in their defense."
Mikhail Tammet, head of IT security at Estonia's defense ministry, told the BBC that the attacks had affected a range of government websites, including those of the parliament and governmental institutions. He said Estonia was particularly vulnerable as much of its government is run online.
"Estonia depends largely on the Internet. We have e-government; government is so-called paperless ... all the bank services are on the Internet. We even elect our parliament via the Internet," Mr Tammet said.
"In the past few weeks it has been quite difficult for some government officials to read their emails on the web and to get access to the banks."
The Estonian defense ministry said that the cyber attacks have come from all over the world, but some have been hosted by Russian state servers, and that instructions on how to carry out cyber warfare are circulating on Russian websites.
Estonian Prime Minister Andrus Ansip has directly accused Russia of being responsible, pointing the blame at the Russian government. Internet experts from NATO and the European Union are helping to track down the culprits, but Estonian officials said that they have had no cooperation from Russia.
Russia — which has a large community of hackers and computer virus-writers — has been accused of mounting such attacks before in the U.S. and Ukraine. Moscow denies any involvement in the Internet attacks on Estonia.
Kremlin spokesman Dmitry Peskov told the BBC that the allegations were "completely untrue."
