The poll results gave the opposition 88 seats, and 87 for parties supporting the center-left government. That would still leave the race open because it doesn't count the four seats from the semi-autonomous territories of Greenland and the Faeroe Islands.
The poll was based on about 6,000 interviews and had a margin of error of about 3 percentage points. Kasper Jensen of polling institute Megafon sounded a note of caution, saying the exit poll wasn't a final result.
Thorning-Schmidt's Social Democrats and opposition leader Lars Loekke Rasmussen's Liberals depend on other parties to build a majority in the 179-seat Folketing, or Parliament. The campaigns focused on immigration and welfare spending, among other issues.
In addition to the 175 seats decided by voters in Denmark, the Faeroe Islands and Greenland get two seats each.
If the vote is close, those four seats could swing a result in favor of either Thorning-Schmidt or Loekke Rasmussen. Currently, the government bloc has three of the four seats. Polling stations in the Faeroes close at 1900 GMT (3 p.M. EDT) while those in Greenland shut down three hours later.
Loekke Rasmussen, a former prime minister, needs support from the populist Danish People's Party, which wants to reintroduce border controls against neighboring countries.
That's a controversial among many in the European Union who feel it would challenge the idea of a borderless Europe. But Loekke Rasmussen appeared to endorse the proposal as he cast his vote in Copenhagen.
"I want an open Denmark, but I also want a Denmark that is efficiently shut for people who don't want our country," Loekke Rasmussen told reporters.
Thorning-Schmidt voted not too far away, accompanied by her husband, Stephen Kinnock, who was elected to Britain's Parliament for the Labour Party in Aberavon last month. He wasn't voting.
"That road we have steered Denmark onto, where we have a grip on the economy, where there is money for the welfare, if that is the way you want to take, then you must vote for the Social Democrats," she said.
Thorning-Schmidt has pledged to raise welfare spending by 39 billion kroner (USD 5.7 billion), while the opposition says that improvements can be achieved without expanding the public sector.
Candidates were campaigning until the very end, handing out leaflets, flowers, balloons and sweets to voters on the streets and squares of the Scandinavian country of 5.6 million. According to pollsters, up to 20 percent of Danish voters had not made up their minds before the election.
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