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Denmark's Prime Minister Mette Frederiksen receives a shirt with the message 'Support Greenland' from Julie Rademacher at a meeting with Greenlanders in Aalborg, Denmark, on Tuesday.Henning Bagger/Reuters

Few European leaders have had a more tumultuous relationship with Donald Trump than Danish Prime Minister Mette Frederiksen, and on Tuesday she’ll be hoping her tough stand against the U.S. President will be rewarded at the ballot box.

Ms. Frederiksen has gained international attention for taking on Mr. Trump over his threats to annex Greenland, a self-governing territory of Denmark. Relations hit a low point this year when Mr. Trump mused about taking the island by force, prompting the Danish military to draw up plans to blow up airstrips in Greenland to thwart a potential U.S. invasion.

She has also made a point of embracing Prime Minister Mark Carney’s call for middle powers to take a more active role in world affairs, as the United States slips further into the role of an erratic hegemon.

Since then, Mr. Trump’s rhetoric about the vast, ice-covered island has cooled.

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The dispute boosted Ms. Frederiksen’s standing in the world and gave her Social Democrats a badly needed lift back home. Last month she moved to capitalize on the country’s animosity toward Mr. Trump by calling an early election.

Throughout the campaign she has portrayed herself as a defender of Danish sovereignty. “We must define our relationship with the United States, and we must rearm to ensure peace on our continent,” she told parliament after calling the election. “As everyone knows, the conflict over Greenland is not over yet.”

Danes head to vote on Tuesday in a general election dominated by concerns over the cost of living, welfare and security.

Reuters

Ms. Frederiksen took a break from campaigning earlier this month to join Mr. Carney and the leaders of Sweden, Norway, Iceland and Finland for a summit in Oslo. During a news conference she referred to Mr. Carney as “Dear Mark” and offered effusive praise of his January speech at the World Economic Forum in Davos, Switzerland, where he urged middle powers to act together “because if we’re not at the table, we’re on the menu.”

“I don’t think I have ever heard so many reflections on a speech from a colleague as I have heard about your speech in Davos,” she told reporters. Denmark, Canada and the other Nordic countries “have to build something new,” she added.

Polls show the election will be close, and Denmark’s fragmented political system means that as many as 12 parties could enter the 179-seat parliament. The Social Democrats are widely expected to win the most seats, but their governing coalition of centre-left parties is forecast to fall just short of a majority. Nonetheless, most analysts predict Ms. Frederiksen will be able to lead a minority government.

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Kasper Hansen, a political science professor at the University of Copenhagen, said the Social Democrats will likely lose several seats on Tuesday, but Ms. Frederiksen has managed to pull the party back from historically low polling numbers last December.

“The bottom line is: Will she actually be able to continue as Prime Minister? And the answer is yes,” Dr. Hansen said. He added that it’s typical for Denmark to have minority governments and that Ms. Frederiksen will move the coalition left or right depending on the issue.

If she can complete a full term in office, she will become Denmark’s longest-serving prime minister since the Second World War.

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Ms. Frederiksen greets well-wishers on the street at Nytorv in Aalborg, Denmark, on Tuesday.HENNING BAGGER/AFP/Getty Images

A win on Tuesday would also cement her reputation as a shrewd politician who cut her teeth in politics at an early age. She joined the Social Democrats’ youth wing at 15 and followed in her father’s footsteps as a union organizer.

She won a seat in parliament at 24 and held a series of cabinet posts before becoming party leader in 2015, after the Social Democrats lost power. She led the party to victory four years later and became the country’s youngest prime minister at 41.

She’s hasn’t been shy about pulling her centre-left party to the right when necessary, especially on immigration.

Her government has introduced some of Europe’s strictest laws on asylum seekers, granting only temporary status to refugees and introducing a swift deportation process. As a result, the number of asylum claims has fallen to the lowest level in 40 years.

That hard line approach neutralized the populist Danish People’s Party and has become a model for other left-leaning governments, including in Britain.

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Ms. Frederiksen is also one of Europe’s biggest supporters of Ukraine and a strong proponent of increased defence spending.

Her international reputation isn’t entirely an asset at home. While Mr. Trump is deeply unpopular in Denmark, domestic issues such as affordability, farm policy and a public outcry over the cancellation of a national holiday have been much higher in voters’ minds.

Ms. Frederiksen’s political fate could also could hinge on how Greenlanders vote.

The island elects two representatives to the Danish parliament along with the Faroe Islands, which is also a self-governing territory. Those four MPs could be kingmakers in a hung parliament.

Both Greenland and the Faroe Islands have been pushing for independence and could use that as leverage in deciding which coalition to back, giving Ms. Frederiksen more to consider if she’s re-elected.

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