MAGDEBURG, Germany—The night after Donald Trump won the presidency, hundreds of backers of an anti-immigrant party whose success has shaken German politics gathered in the biting cold in this eastern German city and celebrated a new reality.

“Bravo, Mr. Trump, you get it!” state party leader André Poggenburg shouted from the stage last Wednesday, framed by the dark hulk of a 500-year-old Gothic cathedral. “Today, I must say, it is truer than ever: Merkel must go!”

“Merkel muss weg! Merkel muss weg! Merkel muss weg!“ the crowd chanted in response. “Merkel must go!”

Mr. Trump’s election is the second upset populist victory in the West this year, after last June’s antiestablishment Brexit vote in the U.K. With it, German Chancellor Angela Merkel, Europe’s most influential defender of postwar internationalism, finds herself further under siege.

The Continent’s populist tide has reached Austria, where an anti-immigrant candidate is polling strongly ahead of next month’s presidential election, and Italy, whose center-left premier could lose a constitutional referendum on which he has staked his career. Aides to Ms. Merkel think in France, nationalist, anti-immigration leader Marine Le Pen could win next year’s presidential election. At home, lingering discontent with Ms. Merkel’s handling of the refugee crisis could spoil her Christian Democratic Union’s re-election bid next fall.

On Thursday, Ms. Merkel met in Berlin with U.S. President Barack Obama. In a subsequent news conference, they vowed to address concerns about globalization that have given rise to populist movements across Europe and the U.S. and helped propel Mr. Trump to victory.

“What unites us is the common conviction that globalization needs to be defined humanely and politically,” Ms. Merkel said. “There is no turning back from it.” She said Germany “will continue to cooperate with the new administration.”

Of all Europe’s mainstream politicians fighting populist insurgencies, Ms. Merkel is in the strongest position. She has relatively high approval ratings and a healthy economy. Allies and opponents agree, though, that she must persuade skeptical voters she can meet a growing pile of political, economic and security challenges at home and beyond.

Ms. Merkel, 62 years old, declined through a spokesman to comment for this article. Aides and allies said in interviews her playbook for pushing back the populist tide includes a reaffirmation of values such as the right to asylum, an admission of past mistakes and the pursuit of pragmatic steps to fix them.

Ms. Merkel is widely expected to announce in the coming weeks she will seek a fourth term in next fall’s election. Current polls show she would be favored to win, although she faces some of the same forces that carried Mr. Trump to victory.

Formerly a political outsider who grew up behind the Iron Curtain, Ms. Merkel has come to embody Germany’s political mainstream, supportive of European integration and American-inspired values of democratic rights and free markets. She faces mounting anger over immigration, security, stagnating wages and sentiment that the political, business and media elite are exploiting the common man.

Last fall, Ms. Merkel opened the country’s doors to thousands of mainly Middle Eastern migrants stranded in Hungary. Many Germans embraced the newcomers. Then, at 12:50 a.m. on Jan. 1, police overseeing revelers at the Central Station in Cologne encountered a crying woman who told them she had been groped. A later government report described a spree of sexual assaults and robberies by migrants that night.

The assaults helped drive an anti-Islam message for parties across Europe. Ms. Merkel’s approval ratings dropped, and the Alternative for Germany, an upstart party critical of Ms. Merkel’s refugee policy, scored unprecedented gains in three state elections in March.

In July, as the refugee stream slowed to a trickle, there were two terrorist attacks by migrants in the space of a week: a teenager injured five people with an ax and a suicide bomber at a music festival injured 15.

“Is Germany now colorful enough for you, Frau Merkel?” populist leader Frauke Petry posted on Facebook in the aftermath. “What more do those in positions of responsibility need in order to open their eyes and recognize what is happening now in Germany?”

When Ms. Merkel held her traditional summer news conference, she repeated her mantra: “We will manage this.”

This month, Ms. Merkel’s approval rating stood at 52%, down from more than 70% in the summer of 2015, according to pollster Infratest Dimap. Her party is polling in the low-30% range, after winning 41.5% of the vote in a 2013 federal election.

“People have a diffuse fear,” said former Bavarian Premier Edmund Stoiber, an elder statesman of German conservatism and a Merkel critic. “You cannot simply address this feeling of insecurity with rational answers. You have to give the people an emotional answer as well.”

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Ms. Merkel was unprepared for the intense emotions stirred by the refugee crisis. “What we learned in the last year is that fundamental achievements of the European Union can be quickly placed into question,” said someone close to her, “and that national animosities can suddenly reappear that we thought were in the past.”

Germany enjoys close to full employment, and its industry has thrived despite economic turmoil elsewhere in Europe. In a recent survey by polling firm Allensbach, more than four-fifths of Germans age 30 to 59 described the quality of life as good or very good. But the share of people who saw the future with fear or skepticism rose to 42%, from 30% last year, while those who looked ahead with hope shrank 14 points to 43%. Their biggest fears were xenophobia, terrorism, the large number of refugees and rising right-wing extremism.

The government counted 10,373 suspected hate crimes in 2015, nearly doubled the prior year’s tally. It blamed the increase mainly on rising xenophobic crime and online hate speech.

In Ms. Merkel’s hometown of Templin, an hour’s drive north of Berlin, Mayor Detlef Tabbert rattled off problems with the new residents: bicycling on the sidewalk and noise late into the evening, challenges in learning German and asylum applicants who can’t even read and write in their native languages.

A local soccer club canceled a trip to Oktoberfest in Munich because of terrorism fears, and the police recently investigated three Afghan asylum applicants for allegedly groping a teenage girl, he said.

Two months ago, mounting criticism of Ms. Merkel within her own party seemed to strike home, people close to her said. Her conservative Christian Democratic Union had just finished behind a populist party to its political right for the first time ever in a state election.

As the results trickled in, Ms. Merkel was in China, fueling critics’ accusations that she is indifferent to the concerns of regular Germans. The next day, Ms. Merkel stepped away from an international meeting to dial into a conference call with her party’s executive board.

Deputy Finance Minister Jens Spahn said the party wasn’t getting through to the people, and suggested that Ms. Merkel had to start showing more empathy for their fears, according to two people familiar with the call. She responded by arguing that support for the party might be stronger if its politicians backed her more visibly.

Within days, Ms. Merkel’s rhetoric began to change. Previously, she had stuck to a twin-track strategy: working to reduce arrivals while exhorting her compatriots to embrace refugees as a positive development for Germany. Now, she began to acknowledge mistakes in her initial handling of the crisis.

Addressing parliament in September, she said, “Germany will remain Germany, with all we cherish and value about it.” Speaking to reporters after the Berlin election later that month, she said she would stop using her much-criticized we-will-manage mantra because it had become “a simple motto, an empty formula.” She even managed a semi-apology for not having seen the refugee crisis coming.

“If I could, I would turn back time many, many years to be able to better prepare myself and the whole government and all those in positions of responsibility for the situation that met us rather unprepared in late summer 2015,” she said.

A crisis team formed in Ms. Merkel’s Chancellery last year to manage the logistics of sheltering the hundreds of thousands of new arrivals is now working to get many of them out of the country. The group has in recent weeks examined increasing the number of days authorities are allowed to keep a rejected asylum seeker in pre-deportation detention, according to a person involved in the deliberations.

The government is betting Germans are more unnerved at the idea of the state losing control of the situation than they are hostile to refugees. Success, not just in reducing the number of arrivals but also in deporting rejected asylum seekers, would show Ms. Merkel is firmly in charge.

Despite the pivot, she stuck to her line that blocking all refugees or all Muslims would contradict not only “the German constitution and our country’s duties under international law, but also, above all, the ethical foundations of the Christian Democratic Union of Germany and my personal convictions.”

On the morning after Mr. Trump’s election, Ms. Merkel and her aides wrote what even they realized was an unusual message for the German chancellor to deliver to the future leader of the U.S.

“Germany and America are connected by values of democracy, freedom, and respect for the law and the dignity of man, independent of origin, skin color, religion, gender, sexual orientation, or political views,” Ms. Merkel said. “I offer the next president of the United States close cooperation on the basis of these values.”

Throughout the U.S. campaign, Ms. Merkel was quietly pulling for Hillary Clinton, whom she knows and respects, people close to the chancellor say. But she never said so publicly, and unlike many other European leaders and members of her own government, she avoided criticizing Mr. Trump.

Ms. Merkel is unruffled by Mr. Trump’s broadsides against her in the campaign, said one of the people close to her. (He called her “insane” for accepting refugees, among other things.)

At the rally of the anti-immigrant Alternative for Germany party last week in Magdeburg, hours after Ms. Merkel’s subtle rebuke of Mr. Trump, her opponents welcomed a new ally in the world’s most powerful office.

“Something became possible today that many people believed was impossible,“ said senior party official Beatrix von Storch. “Everything is possible. We can accomplish everything, even the completely unthinkable.”