Denmark's Prime Minister Mette Frederiksen suffered an election setback on Tuesday, with her left-leaning bloc falling short of a governing majority, setting up tough coalition talks in the weeks ahead.

Frederiksen's Social Democrats and Denmark's other left-leaning parties did not secure sufficient support for a clear mandate to govern in an election held against the backdrop of geopolitical tensions with the United States over Greenland.

The Social Democrats won the most votes and were projected to take 38 of 179 seats, down from 50 four years ago, making this election result the party's weakest showing since 1903, according to early results.

Projections by local media showed the left-leaning "red bloc" would win 84 seats, six shy of the 90 needed for a majority, while the right-leaning "blue bloc" would take 77.

Speaking in Copenhagen's parliament building early on Wednesday, Frederiksen told supporters that assembling a government would be "difficult" and downplayed her party's dip in support after a series of external shocks. "We've had to deal with war, we've been threatened by the American president, and in those almost seven years we've gone down 4 percentage points. I think that's OK," Frederiksen said.

In office since 2019, the 48-year-old had campaigned on her ability to steer the Nordic country through a fraught relationship with Washington and Europe's response to the Russia-Ukraine conflict.

But on Tuesday, she took hits from both the left and the right at home, as the cost-of-living squeeze topped voter concerns, analysts said.

The result lays a path toward some hard coalition bargaining in the weeks ahead, with Foreign Minister Lars Lokke Rasmussen's center-right Moderates, on 14 seats, positioned as kingmaker.

According to CNBC, Rasmussen said: "We're standing in the center. Don't sprint out towards the corner flags. We're standing there in the middle. That's where the game is interesting. Come and play with us."

The vote drew close attention in Greenland, where many hoped to use Trump's interest in taking control of the Arctic island to secure concessions from Copenhagen, Reuters reported.