(CNN) The mass killing at a Pittsburgh synagogue, the deadliest anti-Semitic incident in US history, has Jewish Americans questioning whether they are now fated to live with the fear and threats at home that their community has long endured around the world.

The attack represents a flagrant challenge to America's core values — that people of every race or religion are endowed with the same inalienable rights. Suddenly, these fundamental beliefs are being tested in a divisive new political era that targets a shadowy concept of The Other: Muslims, Mexicans, Middle Easterners.

On Saturday morning -- the Jewish Sabbath -- a gunman shattered the sense of belonging for Jews in America, too.

This cannot be a coincidence: A heavily armed man burst in on a Jewish religious ceremony and killed 11 people before telling a law enforcement officer "I just want to kill Jews" after a week that was heavy with other acts of extremist violence motivated by politics.

Throughout history, anti-Semitism has often been an early indicator that extremist thought is gathering momentum inside a society or is being used as a political tool by those keen to exploit resentment or radical sentiment.

It is an increasingly urgent question whether President Donald Trump's deliberately divisive politics may be giving license to extremists.

He cannot be accused of being directly to blame for horrific incidents like the one this weekend. And on Saturday, he delivered a welcome and passionate condemnation of the attack in Pittsburgh, calling anti-Semitism a "vile hate-filled poison" and "one of the ugliest and darkest features of human history."

The President is not stepping back. He responded to growing debate about his contribution to the toxic political atmosphere Monday with one of his most inflammatory Twitter attacks yet on journalists.

"There is great anger in our Country caused in part by inaccurate, and even fraudulent, reporting of the news. The Fake News Media, the true Enemy of the People, must stop the open & obvious hostility & report the news accurately & fairly," he wrote.

The tweet represented a characteristic attempt by the President to exploit tensions and name an enemy in a bid to consolidate his power among his own supporters.

Trump has in the past used tropes and language known to appeal to a tiny minority of extremists who might contemplate violence. Trump has recently taken to proclaiming he is a "nationalist" a nd berated "globalists" -- two designations that have innocent connotations in some contexts but are also recognized as code words by anti-Semites.

Events of the last week have called into question the President's warnings in a jarring closing argument to his midterm campaign that the greatest threat to Americans comes from a migrant caravan 1,000 miles to the south of the US border in Mexico.

Hatred of Jews and refugees

Social media posts suggest that Robert Bowers, the alleged gunman in Pittsburgh, claimed that Jews were helping transport members of the migrant caravan in Mexico. For the last two weeks, Trump has been arguing that the column contains "bad people" and Middle Easterners -- a code word for terrorists.

Bowers also condemned the Hebrew Immigrant Aid Society (HIAS), which brings refugees to the US. His attack bears the hallmarks of an outrage motivated by hatred of Jews and refugees.

But it did not occur in isolation.

Recent years have seen a rise in anti-Semitic incidents across the country and the use of coded anti-Semitic imagery in material by right-wing politicians, including some prominent members of the Republican Party.

Yet most top political leaders have not yet felt the need to go out of their way to comprehensively condemn this new wave of extremist thought, despite evidence the problem is worsening.

The Anti-Defamation League found a 57% increase in anti-Semitic incidents in 2017 compared to the previous year, including hate speech in schools and colleges, vandalism and bomb threats.

Such figures suggest that while the United States has been seen as largely immune from anti-Semitic feelings that have long simmered in politics in some European nations, things could be changing.

Anti-Semitic themes have also been increasingly cropping up in political campaigns, raising the possibility that some leaders see advantage in using such imagery to connect to radical voters while preserving deniability.

In 2016, a closing Trump campaign advertisement blasting a global establishment elite portrayed three people as villains alongside Hillary Clinton: billionaire liberal financier George Soros, former Federal Reserve Chair Janet Yellen and Lloyd Blankfein, the chairman of Goldman Sachs. All are Jewish.

Trump's own daughter Ivanka and son-in-law Jared Kushner are practicing Jews. Many of Trump's past business associates and lawyers are Jewish. So it's not credible to argue he is an anti-Semite. Yet he still sometimes attacks Soros despite knowing that the Hungarian-born philanthropist is a hate figure and Jewish stereotype for anti-Semites and extremists on the far right fringes.

Trump: 'There is no blame'

Hints of anti-Semitism are also evident in some other GOP messaging.

Republican House Majority Leader Kevin McCarthy this week deleted a tweet accusing Soros, former New York Mayor Michael Bloomberg, and Tom Steyer of trying to buy the midterm elections for Democrats, after a bomb was mailed by a Trump supporter to Soros. All three men are Jewish or of Jewish descent.

Iowa GOP Rep. Steve King recently endorsed Faith Goldy, a nationalist running for mayor in Toronto, who claims Canada is facing a "white genocide" and who has promoted anti-Jewish material.

The recent incidents in Pittsburgh and elsewhere raise urgent questions about whether inflammatory rhetoric that appeals to extremists translates into violence.

Vice President Mike Pence denies any such link.

"Everyone has their own style, and frankly, people on both sides of the aisle use strong language about our political differences," Pence told NBC News in an interview Saturday. "But I just don't think you can connect it to acts or threats of violence."

Trump was asked on Friday whether he bore any responsibility after a Florida man, Cesar Sayoc, allegedly sent the mail bombs.

"There is no blame. There's no anything," he told reporters on Friday.

But Mark Hetfield, president and CEO of the Hebrew Immigrant Aid Society, said that there is a growing acceptance of rhetoric that can endanger lives and that America's leaders must take a stand.

"The problem here is hate. The problem is there is a growing space in this country for hate speech and hate speech always turns into hate action," he told CNN on Saturday night.

"We cannot stand by as individuals or organizations or as governments when people spew hatred against, Jews, refugees, Latinos, against any group that some see as the other," Hetfield said.

Trump, who this week plans a major speech on securing the border, has used the idea that Americans are under threat from outsiders as an organizing principle of his campaigns.

He has stigmatized some Mexicans Muslims refugees, and Africans — contributing to fervor on the right — all while accusing Democrats of trying to whip up "mob rule."

So while his fervent condemnation of anti-Semitism sent a strong message, the President is on less firm ground on the question of whether his rhetoric is providing space and encouragement to extremist views.

"All politicians and public figures are role models and none more so than the American President," said Ruth Ben-Ghiat, a professor of history at New York University who has written extensively about the common characteristics of strongmen leaders.

"The problem is that Trump has made it clear since the campaign that the public he is speaking to, the public he wants to impress, that he cares about, is a public that is not interested in human rights, in democracy and in loving one's neighbor."