Four decades after the landmark ruling was handed down, making abortion legal under most circumstances throughout the United States, 63 percent of respondents said they would not like to see a court overturn the decision, while 29 percent said they would.
These opinions are little changed from surveys conducted 10 and 20 years ago, Pew said in a statement.
Michael Dimock, director of the Pew Research Center for the People and the Press, told Reuters it was uncommon to see views remain basically unchanged on such a controversial issue.
"They really haven't changed a lot over the years which is kind of interesting because a lot of other social issues have changed a lot, gay marriage being the most notable example," Dimock was quoted as saying.
According to the Los Angeles Times, 53 percent of those surveyed said abortion “is not that important compared to other issues,” compared with 48 percent in 2009 and 32 percent in 2006, suggesting there are more pressing issues such as national debt and gun ownership.
The percentage of people viewing abortion as a “critical issue facing the country” fell to 18 percent from 28 percent in 2006, Pew said.
Pew also found that only 44 percent of Americans under the age of 30 know that Roe v. Wade was a Supreme Court case dealing with abortion rather than another rights issue.
The 40th anniversary of the decision, which established a woman’s constitutional right to abortion at least in the first three months of pregnancy, will be on January 22.