Opinion polls put Prime Minister Anders Fogh Rasmussen's Liberal-Conservative bloc, offering tighter immigration laws and tax cuts, slightly ahead of the Social Democrats, who have pledged to improve the welfare system.
Eight political parties will have to overcome the 2% margin to make it into the 179-seat legislature.
Rasmussen, running for a third term, insists that better social care can be brought about despite tax cuts. "Lower taxes will not lead to lower funding for schools, hospitals, kindergartens and retirement homes," the governing coalition said in a campaign slogan.
However, the four-party opposition Social Democrats led by Helle Thorning-Schmidt have insisted better welfare will be impossible under lower taxes.
A survey conducted by pollster Capacent Epinion on the day before the election showed Rasmussen's three-party bloc had the support of 28% of the electorate, implying 89 seats, narrowly ahead of the Social Democrats with 26.3%.
With the small margin, Rasmussen's coalition may have to garner support from two smaller parties, the nationalist Danish People's Party and the New Alliance led by Syrian-born Naser Khader, to maintain a sufficient majority in parliament.
An opinion poll conducted for Danmarks Radio said New Alliance had the support of 2.9% of voters and could gain five seats.
The previous elections were held two years ago but Rasmussen decided to call new elections in October before his four-year mandate expired, taking advantage of the favorable economic and political situation in Denmark.
