By Daniel Burke, CNN Belief Blog Co-editor

(CNN) - The number of nonreligious Jews is rising in the United States, with more than one in five saying they are not affiliated with any faith, according to a new survey.

While similar trends affect almost every American religion, Jewish leaders say the new survey spotlights several unique obstacles for the future of their faith.

According to the survey, conducted by Pew Research Center's Religion & Public Life Project, non-religious Jews are less likely to care deeply about Israel, donate to Jewish charities, marry Jewish spouses and join Jewish organizations.

Pew says their study sought to explore the question, "What does being Jewish in America mean today?" The answer is quite complicated.

Just 15% of American Jews say that being Jewish is mainly a religious matter, according to Pew's survey. By contrast, more than six in 10 say Jewishness is about culture, ancestry and identity.

The most essential parts of being Jewish, according to American Jews, are remembering the Holocaust (73%), leading an ethical life (69%) and working for social justice and peace (56%).

Almost as many American Jews say that having good sense of humor (42%) is as important to their Jewish identity as caring about Israel (43%).

Even among religious Jews, most say it's not necessary to believe in God to be Jewish, and less than one in three say religion is very important to their lives.

Nearly all American Jews - religious and secular - say they are proud to be Jewish.

"The fact that many Jews tell us that religion is not particularly important to them doesn't mean that being Jewish is not important to them," said Greg Smith, director of religious surveys for the Pew Research Center.

The most essential parts of being Jewish, according to the survey, are remembering the Holocaust (73%), leading an ethical life (69%) and working for social justice and peace (56%).

Overall, the majority of Jews (78%) call themselves religious, but the survey showed much lower rates of religious affiliation among millennials, one of several trends that trouble Jewish leaders.

Nearly a third of American Jews born after 2000 answered "none" when asked about their religious affiliation, suggesting that Jewish "nones" are not only a large group, they're growing, Smith said.

The rise of Jewish "nones" tracks with wider trends in the American population, where about a third of millennials don't affiliate with organized religion.

The nonpartisan Pew Research Center says its survey is the most comprehensive since the National Jewish Population Survey in 2000-2001.

Pew surveyed 3,475 Jews from across the country from February 20 to June 13, with a margin of error for the full sample of plus or minus 3 percentage points.

The study declines to offer a definitive estimate of the size of the American Jewish population, a matter of heated debate in recent years.

Instead, Pew offered several tallies of American Jews, depending on different definitions of Jewish identity.

Approximately 4.2 million American adults - 1.8% of the overall population - identify as Jewish by religion. In the 1950s, the percentage of religious Jews in the United States was nearly twice as high, according to Pew.

Meanwhile, about 1.2 million adult Americans now identify as secular or cultural Jews - they were raised Jewish, had a Jewish parent and still consider themselves Jewish, even though they don't practice the religion, according to Pew.

Secular Jews are much more likely to marry outside the faith, according to Pew, a trend that has worried Jewish leaders in recent years.

Nearly 60% of American Jews who have married since 2000 have a non-Jewish spouse, according to Pew.

Intermarried Jews, like secular Jews, are much less likely to raise their children in the Jewish faith and have weaker ties to the Jewish community, says Pew's report.

But, in a silver lining for Jewish leaders, intermarriage rates have leveled off, Smith said, holding steady at 60% since the mid-1990s.

Jane Eisner, editor-in-chief of the Jewish Daily Forward, said she is not surprised that the study found relatively low interest in Jewish religious beliefs.

"We are a people very much defined by what we do, rather than what we believe," she said.

But Eisner said she is concerned that millennials are less likely to donate to Jewish charities, care strongly about Israel or belong to Jewish groups.

"It's great that these non-religious Jews feel pride in being Jewish," Eisner said. "What worries me is their tenuous ties to the community."