Washington (CNN) -- A major figure in the project to build an Islamic center and mosque near ground zero in New York City said Sunday that moving the project to another site is not under consideration for now.
Daisy Khan, who is heading the development of the project with her husband, told ABC's "This Week" that a move could be considered after consultations with "all major stakeholders" take place.
"We will meet and we will do what's right for everyone," Khan said, noting the project has the backing of the community board as well as New York Mayor Michael Bloomberg and other politicians.
Moving from the planned site two blocks from where al Qaeda attackers destroyed the World Trade Center, killing more than 2,700 people, raises constitutional issues and would be noted by Islamic extremists, Khan said.
"We have to be very careful and deliberate in making any move," Khan said.
The issue has become an emotional topic in the United States, with conservative Republicans and some families of victims leading an effort to prevent the Islamic center and mosque from being built.
A protest against the project was scheduled to take place Sunday in New York.
President Barack Obama, Bloomberg and others, including a group representing some families of victims of the September 11 attacks, have supported the right of Khan's group to build the facility near ground zero.
Khan appeared on the program with Rabbi Joy Levitt, the executive director of the Jewish Community Center in New York. Khan said the facility she and her husband, Imam Feisal Abdul Rauf, are developing would be modeled after the Jewish Community Center.