President Paksas had urged people to vote
The people of Lithuania have voted to join the European Union.
More than 91% of voters who took part in a two-day referendum in the Baltic state said yes.
Around 63% of the country's 2.7 million registered voters took part.
Election officials had suggested voter apathy could mean less than half of the electorate would vote, thus making the referendum invalid.
But by Sunday afternoon, officials said they believed the vote was on course for legitimacy.
"The data we have now shows that by the end of the day the
referendum will be valid," a senior election official.
After the first day of voting on Saturday, only 30% of voters had cast their ballots.
Lithuania, which has a population of 3.5 million, is one of 10 mostly ex-communist states hoping to join the 15-nation EU next year.
All major political parties in the Baltic republic are in favour of joining the European bloc.
The BBC's Steve Rosenberg says if Lithuania does join the EU it will have come a long way since 1990 when it was still part of the Soviet Union.
In that same year, the country declared its independence from Moscow.
On Saturday, President Paksas urged Lithuanians to cast their votes.
"Our neighbours, the Latvians and Estonians, and other European countries are watching us as they did in the 1990s when we were the first to declare independence," he said.
"The situation is under control, and... I think we will be able to cross the barrier," the president added.
Parliamentary Speaker Arturas Paulauskas said that most
residents had "gone to plant potatoes" on Saturday, a traditional work day.
The data we have now shows that by the end of the day the referendum will be valid
Zenonas Vaigauskas, head of the election committee
Opinion polls taken before voting began suggested Lithuanians would support EU entry - even though not everyone is happy with the idea - if enough people turned out to cast their ballots.
Some farmers resent the fact that Lithuania will receive smaller agricultural subsidies than existing EU states.
Lithuania is the fourth EU candidate to hold a referendum on joining, after 10 states were invited last year to join the bloc in May 2004.
Malta, Slovenia and Hungary all voted "yes" earlier this year.