"Exit polls so far are definitely suggesting a shift towards a 'Yes' vote, particularly in working class and inner-city areas which came out in force for a 'No' vote last time," an official with the governing Fianna Fail party told the agency.
The treaty, aimed at streamlining decision-making in the enlarged bloc, cannot take effect unless all the member states ratify it.
Around three million Irish citizens were eligible to vote on Friday.
Irish Prime Minister Brian Cowen urged voters to go to the polls: "It is an important day for the country and an important referendum... I'd ask everybody, we all have rights as citizens, and one of the rights that should be cherished is our right to vote."
Dr Paul Duffy: A No vote would 'create a lot of uncertainty'
At the Redeemer Boys' School in Dundalk, County Louth, enthusiasm amongst voters appears to be muted, with barely 25% of the electorate voting by late afternoon, the BBC's Chris Mason reports.
In Louth, 250 jobs have been lost recently at the Coca-Cola factory, with further redundancies at Xerox - in a region that voted strongly No last time.
But being close to the UK border, there are strong Republican sympathies here. Some argue that having fought for Irish independence it would be reckless to hand more power to Brussels, our correspondent adds.
Apart from Ireland, the only other countries yet to ratify Lisbon are the Czech Republic and Poland. Despite opposition calls for a referendum in the UK, the treaty has been ratified there by parliament.
All of Ireland's major parties campaigned for a Yes vote except the nationalist Sinn Fein. The party believes rejecting the treaty would secure a more democratic EU.
Sinn Fein's Mary Lou McDonald on the Lisbon Treaty
Its leader Gerry Adams said: "Citizens want a fairer Ireland, a fairer Europe, a democratic Ireland, a democratic Europe.
"If we want to have decency and accountability and if we want a social Europe then come out... and vote No."
The Yes camp also had some lavish donations from big business.
The repeat referendum is about the same treaty text, but since last year EU leaders have given specific commitments on issues which made some Irish voters nervous last time.
The country will not be forced to legalise abortion, to lose control over taxation and will not have its neutrality threatened.
The chances of the treaty being rejected a second time appear pretty slim, says the BBC's Jonny Dymond, in Dublin.
Ireland's economic situation is so grim, he adds, that many voters are unwilling to risk further turmoil with another No vote, and while many would dearly love to punish the hugely unpopular administration, most will hold off until the next election.
However, opponents continue to maintain that Lisbon undermines national sovereignty and concentrates too much power in Brussels.
Ratifying the treaty would bring in some major changes within the EU.
It would expand the policy areas subject to qualified majority voting (QMV), rather than unanimity. It would also establish a new post of president of the European Council - the grouping of EU states' leaders - and a high representative for foreign affairs.
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