By Anton Troianovski

BOCHOLT, Germany—Martin Schulz, the Social Democratic candidate for chancellor of Germany, worked up a crowd at a rally this week by recalling his party’s defiant opposition to the Nazis and exhorting them to confront what he said was another malign force: U.S. President Donald Trump.

Mr. Trump’s “attacks on Europe are also attacks on Germany,” Mr. Schulz said. “In a time when the world is drifting apart, in a time of Trumpism, we need values-based cooperation of the democracies in Europe now more than ever.”

Such rhetoric has helped the 61-year-old Mr. Schulz, until recently the president of the European Parliament, set himself apart from the long-dominant force in German politics, Chancellor Angela Merkel, as the country embarks on campaigning for a general election in September.

A survey conducted by the polling firm INSA for the Bild newspaper and released Monday showed his party, known as the SPD, ahead of Ms. Merkel’s conservatives for the first time in more than five years.

Mr. Trump’s victory in U.S. elections in November energized his ideological allies in Europe’s antiestablishment parties. But Mr. Schulz’s case shows it could also end up boosting support for centrist politicians who oppose the new American president’s policies.

More than 75% of Germans disapprove of Mr. Trump’s record so far, according to another INSA/Bild poll. A third survey, by Infratest Dimap, found that since Mr. Trump’s election, the share of Germans who consider the U.S. to be a trustworthy partner has fallen to 22% from 59%.

The anti-immigrant and antiestablishment Alternative for Germany, which has praised Mr. Trump, has struggled in the polls recently. It dropped to 12% in this week’s INSA poll, compared with 15% in early January.

It is unclear how broad and durable the fallout from Mr. Trump’s rhetoric and policies will be among voters and politicians in Europe, and whether it will result in the widespread anti-American feelings that swept Europe before and after the 2003 invasion of Iraq.

British Prime Minister Theresa May, who traveled to Washington to cement her country’s “special relationship” with the U.S. shortly after Mr. Trump took office, has faced criticism from her opponents.

More than 1.8 million people in the U.K. have signed a petition calling on Mrs. May’s government to cancel or downgrade a planned state visit by Mr. Trump.

On Monday, the speaker of the British House of Commons, John Bercow, said he opposed allowing Mr. Trump to address Parliament.

“I feel very strongly that our opposition to racism and to sexism and our support for equality before the law and an independent judiciary are hugely important considerations,” he said.

On many issues, Mr. Schulz’s positions are similar to those of Ms. Merkel: He largely supported her acceptance of refugees and sanctions against Russia over the crisis in Ukraine. But his willingness to speak out bluntly against Mr. Trump has been a big difference.

Ms. Merkel, who allowed hundreds of thousands of refugees and migrants from the Middle East and North Africa into Germany in 2015, has been a frequent target of Mr. Trump’s attacks.

The chancellor, however, has avoided responding in kind and has sought to highlight possible areas of cooperation.

After Mr. Trump called her refugee policy catastrophic, she said: “He has presented his positions once more—they have been known for a while. My positions are also known.”

Mr. Schulz’s rhetoric, in contrast, has been sharp. “What the U.S. government is starting right now is a cultural struggle,” Mr. Schulz said in an interview in Saturday’s issue of Der Spiegel magazine. “We should confidently take up this struggle and say: We have a different model for society.”

The magazine’s cover showed Mr. Trump brandishing a bloodstained knife and holding the severed head of the Statue of Liberty.

Mr. Schulz “is using the greater freedom that he has” as a candidate rather than a head of government to pressure Ms. Merkel, INSA chief Hermann Binkert said. “She can’t act as undiplomatically.”

Speaking to SPD members in this town near the Dutch border on Monday, Mr. Schulz delivered a paean to past comrades who voted against a 1933 law that paved the way for Hitler’s dictatorship.

The Nazis’ “methods were visible in part in the U.S. campaign, by the way—slander, malevolence, intimidation,” Mr. Schulz said. He quoted the British statesman Edmund Burke: “The only thing necessary for the triumph of evil is for good men to do nothing.”

Then he told the crowd: “Today, I think we are called upon to do something good.”

The aggressive approach is allowing the Social Democrats to draw a contrast to Ms. Merkel, something they have struggled to do over the past three years as the junior partners in her government.

Ms. Merkel leads the conservative Christian Democrats but has adopted many policies popular on the left, from accepting refugees to enacting a minimum wage and rejecting nuclear energy.

If the Social Democrats finish first in the election, Mr. Schulz would be highly likely to become chancellor, but he would almost certainly need a governing partner to form a majority. It could recast a coalition with Ms. Merkel’s conservatives or shift to one with the Greens and the far-left Left.

Even if the Social Democrats don’t finish first, they could still try to form a left-of-center coalition if they, the Greens, and the Left combined manage to secure more than half the seats in parliament.

Taking on Washington plays well with the Social Democratic base. In 2002, then-Chancellor Gerhard Schröder of the Social Democrats won re-election in part because of his loud opposition to a U.S.-led invasion of Iraq.

Ms. Merkel’s allies and supporters counter that uncertain times demand the steady hand of the chancellor, who has been in power since 2005.

Elisabeth Hakvoort, 66, said that while Ms. Merkel was “a bit more careful” in addressing Mr. Trump than Mr. Schulz has been, she had the experience to take the right approach.

Werner Moschüring isn’t convinced. The retired Volkswagen worker said after a decade of not voting, he may cast his ballot for the Social Democrats this year. Mr. Schulz, he said, would be the right man to take on Mr. Trump.

“He has a tougher approach,” Mr. Moschüring said. “Merkel is too squishy.”