COTTBUS, Germany — Germany’s far-right party made significant gains in elections in two of the country’s eastern states on Sunday, exit polls showed, but it failed to surpass establishment parties to gain the biggest portion of the vote, as some had predicted.

Residents of Brandenburg, which surrounds Berlin and Saxony, on the country’s eastern border with Poland and a stronghold of support for the right-wing Alternative for Germany (AfD) party were voting to elect representatives for their state legislatures.

But while exit polls showed a surge in support for the right-wing party, it was predicted to come in second in both states. Angela Merkel’s Christian Democratic Union won 32 percent of the vote in Saxony, exit polls showed; AfD took 27.5 percent.

The Social Democratic Party, the CDU’s coalition partner in the national parliament, was expected to remain the largest party in Brandenburg, with 27.5 percent of the vote to 22.5 for the AfD.

The results weren’t as bad for Germany’s traditional parties as they had feared, but still showed a significant shift to the far right, which drew out new voters in an election with greater than usual turnout.

“One thing is clear from these results: The AfD came to stay,” Andreas Kalbitz, the AfD leader in Brandenburg, said at an election party. In recent days he acknowledged attending a neo-Nazi rally in Greece a decade ago after a leaked report in Der Spiegel. He said he had done so out of “curiosity.”

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“Politics without us is no longer possible,” he said.

It was the first time those living in the eastern regions voted for their representatives in the state-level parliament, known as the Landtag, since Merkel opened Germany’s doors to more than a million refugees, many of them fleeing the civil war in Syria. While many Germans approved the decision, it has also caused a backlash. Immigration has become a rallying point for the AfD.

The party has also tapped into resentment among the people of the former East Germany, which still suffers from higher unemployment and lower wages and pensions than the West, 30 years after the country’s reunification.

Many of those voting said immigration was the most important issue for them.

Cottbus, Brandenburg’s second largest city, lies 80 miles southeast of Berlin, the capital, in the heart of Germany’s coal region. At one polling site, a 50-year-old shop assistant and her husband said they cast their ballots for the AfD.

“We want our country to be open to the world, but only for people who respect our culture and way of life,” she said. “Being AfD doesn’t mean being Nazi. We are not Nazis.”

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The couple declined to be named, saying that voting for the AfD can be stigmatized.

Professor Hans Vorländer, director of the Mercator Forum for Migration and Democracy at the Dresden University of Technology, said the results were “primarily a win for the AfD, though they didn’t reach their goal to become the strongest party.”

Vorländer said the results didn’t necessarily show support for the major parties, but reflected voters casting their ballots for them in an attempt to block the AfD.

Michael Keil, a 34-year-old business administration student, voted for the Green Party.

“It’s important to vote to counter the AfD,” he said. He said people in the former East Germany have little experience of foreigners and “they just vote on fear.”

A majority in western Germany supported Angela’s decision to open the country to largely Middle Eastern refugees in 2015, but a majority in the east opposed it.

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“We have two party systems,” Vorländer said. “One for the east and one for the west.”

The left-wing Die Linke was previously the anti-establishment party in the east, he said, but now the AfD is filling that role. Exit polls showed Die Linke losing 8.4 percentage points in Saxony and 7.4 in Brandenburg.

For the region’s newest residents, it’s a worrying trajectory. Sayed Walid, a 25-year-old asylum seeker from Afghanistan who has lived in Cottbus for three years, said the growth in support for the AfD was a concern.

“If they win,” he said, “I don’t know what will happen to people like us, what the future of the country will be, what the reaction of the people will be.”

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