The Pew Research Center survey found 81 percent of U.S. Muslims have heard about the project and, of those, 72 percent say it should be allowed to be built.
At the same time, 20 percent of the country's Muslims say it should not be allowed to be built, while 15 percent say it should be allowed even though they personally believe it's a bad idea to build it near the World Trade Center site, the survey found.
The survey revealed a decidedly different view among the general public. Of about 78 percent who heard of the project, only 38 percent said it should be allowed to be built, while 47 percent said it should not.
The mosque and Islamic center would be built just 2 blocks from where the World Trade Center stood before being destroyed in the 2001 terrorist attack by al-Qaida.
Asked about mosques or Islamic centers in their community, 14 percent of U.S. Muslims said there had been opposition to building a mosque in the past few years and 15 percent said a mosque or Islamic center in their community has been vandalized or a target of other hostility in the past 12 months, the survey found.
The survey was based on telephone interviews of about 1,075 people and had a sampling error of plus or minus 5 percentage points.
Celebrity Families of 2014 [PHOTOS]