With 60 per cent of votes counted, Rasmussen's coalition and the DPP were hovering close to the 90 seats needed for a majority, while the opposition was on course to win 81.
New Alliance, created earlier this year by Syrian-born Naser Khader in a bid to reduce the DPP's influence on the government, was set for five seats, support Rasmussen would need should he fall short of a clear majority.
Meanwhile, festivities at the Liberal party's election-night venue started as the projections rolled in.
"The way it's looking, the Liberals are right now positioned to stay in power," said Morten Dahlin, 18, a member of the Liberal youth.
"It's not too early to party." Thor Petersen, the finance minister of the Liberal Party, said.
"It looks like the government will be the same tomorrow".
Asked if it was time to start celebrating, he said "yes."
Rasmussen, in power since 2001, campaigned on his strong economic record, arguing that country's robust economy with record low unemployment was the best guarantor of the Danes' cherished welfare state.
"We have had six years of economic growth and stability and we are asking voters for a new vote of confidence to continue our work," he said on Tuesday.