By Dan Merica, CNN

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Washington (CNN) - Forty years after the Supreme Court protected abortion rights in Roe v. Wade, a new survey finds that white evangelicals remain the only major religious group that supports overturning the landmark ruling, even though most such groups find abortion morally wrong.

Slightly more than half (54%) of white evangelicals, according to the Pew Research Center study, favor completely overturning the 1973 Supreme Court decision that affirmed a woman’s right to have an abortion. No other religious group, including white mainline Protestants, black Protestants and white Catholics, agreed with completely overturning the ruling.

In fact, substantial majorities of white Protestants (76%), black Protestants (65%) and white Catholics (63%) say the ruling should not be over turned, the survey found.

But support for keeping Roe v. Wade intact does not mean these religious majorities believe abortion is morally acceptable.

A majority of every religious group sampled - white evangelicals (73%), black Protestants (58%) and Catholics (58%) and a plurality of white mainline Protestants (36%) - responded that abortion was morally wrong. Those respondents who find it morally wrong are also overwhelmingly likely to support overturning the law, compared with keeping it intact - 85% to 5%.

"What is interesting about this aspect of abortion attitudes is that while many people find abortion to be problematic, they may either personally feel it is wrong or favor greater restrictions. Overturning Roe v. Wade is not nearly as supported an idea," said Michael Dimock, director at the Pew Research Center. "The vast majority of evangelicals say they see abortion as morally wrong, but barely a majority say that they want to see Roe v. Wade overturned."

Dimock points out that while more than 70% of white evangelicals find abortion morally wrong, only slightly more than 50% say the ruling should be overturned. "There is somewhere in the neighborhood of 20% of evangelicals who are personally opposed to abortion but don’t want to see this precedent changed," Dimock said.

The religiously unaffiliated were the only group in which more people say they find abortion morally acceptable rather than wrong. Twenty-four percent of the group said it was acceptable, compared with 20% who said it was wrong. Nearly half (43%) said it was not a moral issue.

White evangelicals (64%) are also the most ardent that abortion should be illegal in “all or most cases.” Mormons (63%) and Hispanic Catholics (53%) are the only other two religious groups where more respondents favor illegality in all or most cases.

“By contrast, nearly nine in 10 Jews say abortion should be legal in all or most cases, as do about seven in 10 Americans with no religious affiliation and 63% of white mainline Protestants,” the survey reported. “Among both black Protestants and white Catholics, 54% say abortion should be legal in all or most cases.”

The establishment of a woman’s constitutional right to terminate a pregnancy has been controversial in the four decades since the Supreme Court decision. The court’s ruling was not close, however. Seven of the nine justices voted in favor of making abortion a fundamental right under the Constitution.

Anti-abortion rights activists have demanded the ruling be repealed, a move that would likely allow states to decide whether to allow abortions or not. With the judiciary becoming more conservative during George W. Bush's presidency, some observers said the court under Chief Justice John Roberts would be anti-abortion activists best opportunity to relitigate Roe v. Wade.

"Roe v. Wade certainly did engage the pro-life movement by being so symbolic of an issue, but I don’t think the level of opposition to abortion has really shifted that much over time," Dimock said. "For a very contentious ruling, the public's view on it has remained fairly stable."

Frequency of religious services attendance is also an indicator of whether a poll respondent wants Roe v. Wade overturned. According to the survey, people who attend weekly or more support overturning the decision by 55% to 44%.

That number is substantially different among respondents who attend church less often. According to the survey, 76% among those don't support overturning the ruling, compared with 17% who do.

The Pew Research Center results are part of a study released with the 40-year anniversary of Roe v. Wade in mind. The telephone survey of 1,502 adults was conducted from January 9 through Sunday, with a margin of error of plus or minus 2.9%.