"For the first time, voting by Internet, away from the polling station, is possible," the national elections commission said in a statement.
Electronic voting will take place over three days ahead of Sunday's local elections, when people will be able to cast ballots in traditional way.
"There was brisk e-voting in the morning when polling time started," Tarvi Martens, project leader for Internet voting at the national elections commission, said.
"So far we've had no technical glitches or anything; everything has run smoothly."
Voters cast their ballots via a secure Internet site, using a microchip equipped ID card that they slide through an electronic card reader attached to a computer.
After selecting the candidate of their choice with a click of the mouse, the voter has to enter the ID card's PIN code and submit the vote.
More than 60 percent of Estonia's population of some 1.33 million have the ID-cards with microchips but very few computer owners have the card reader.
Estonia has pioneered the use of new technology in the public sector.
With machine-readable ID-cards, pre-filled electronic tax-forms, parking by mobile phone and paperless government sessions, some have said that the country should change its name to e-stonia.
Estonia is also home to Skype, the popular computer software that enables the user to make free phone calls all over the world.
"The Internet has already entered the realm of politics in many ways," said Ivar Tallo, head of the e-Governance Academy, a training and research group for introducing electronic tools to promote democracy.
"E-voting is another important step to show how the mechanisms of democracy are changing in front of our eyes. This is a major change," he said.
Prime Minister Andrus Ansip was among the first to use the new system of voting on Monday when he cast his ballot from his office computer, in the presence of reporters.
"I decided to vote electronically to try out this new thing," Ansip said.
"Since I'm not in my home town on polling day, Internet voting gives a good chance to plan my time. The whole procedure took just a few minutes and was very comfortable and simple."
Ansip said that Internet voting has been tried before in other places but "few are the countries where such a method has been used nationwide".
"I believe electronic voting helps highlight the other excellent electronic solutions available to citizens in this country."
If the electronic voting system works well in the local elections, parliament is set to amend Estonia's statute books to allow the same method to be used in legislative elections, due in 2007.
Estonia's system of Internet voting was exemplary for its security, Martens of the election commission said.
"In Switzerland people receive their PIN codes via the postal system, but in Estonia there is no need for such relatively insecure moves as ID card holders have their PIN codes already," he said.
"The whole idea is to make voting as simple as possible."
© 2005 Agence France-Presse
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