Defence Minister Troels Lund Poulsen from the liberal Venstre party could emerge as a consensus figure, as could Foreign Minister Lars Lokke Rasmussen of the centre-right Moderates.
Mette Frederiksen
Frederiksen embodies the revamped Social Democrats, committed to a hard line on migration to defend the country's cherished welfare state.
The 48-year-old has been an MP since the age of 24 and took over as the leader of Denmark's biggest political party in 2015 after the country's first female prime minister, Helle Thorning-Schmidt, stepped down following an election loss.
Frederiksen first headed a minority government made up exclusively of Social Democrats from 2019 to 2022.
Initially she was hailed for the government's handling of the Covid-19 pandemic, but ran into trouble with what became known as the "mink crisis" -- a government-ordered cull of roughly 17 million minks over health concerns that was ruled illegal.
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Frederiksen has led a left-right coalition in her second term, adopting tougher migration policies to counter the rise of the far right.
She has given solid support to Ukraine and squared off against US President Donald Trump over his bid to annex Denmark's autonomous territory Greenland.
Hailing from a long-standing Social Democratic family, she is the daughter of a typographer and a pre-school teacher.
Troels Lund Poulsen
Frederiksen had barely called the election at the end of February when Lund Poulsen, 49, threw his hat into the ring.
The Venstre leader has spent four years working alongside Frederiksen, first as economy minister then defence.
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Now he wants to lead a right-wing coalition to power, saying he fears a left-wing coalition led by the current prime minister would "swamp Danes and our businesses with new, high taxes".
Unlike Frederiksen, Lund Poulsen is not inclined to share his life on social media, and while he has years of experience in several cabinets, few expected the current deputy prime minister to be a candidate for the top job, according to Danish media.
He has acknowledged that he even considered withdrawing from political life in 2022, saying he was exhausted.
Described as an uncompromising defence minister, he has overseen the beginning of Denmark's rearmament in response to a perceived threat from Russia and tensions over Greenland.
Lars Lokke Rasmussen
Having already served as prime minister twice, Lokke, as he is widely known, seems at home in the spotlight.
He recently posted a photo of himself on Instagram with a goat, which commentators interpreted as his desire to proclaim himself the "GOAT" (Greatest Of All Time).
A seasoned foreign minister, Lokke was on the front line in recent negotiations after Trump insisted the United States needed to take control of Greenland.
Born in central Denmark to a stay-at-home mother and a father who was an accountant, he trained to be a lawyer before entering parliament in 1994.
He was a member of Venstre for 40 years, but left the party in 2021 to create the Moderates party, which then managed to become part of Frederiksen's government after their first election campaign in 2022.
A skilful politician, he has weathered several storms, including a scandal over his use of party funds to buy expensive suits.
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