"We would undercut the values and principles that so many heroes died protecting," Bloomberg said at the dinner Tuesday in observance of Iftar, the breaking of the daily fast during Ramadan.
The mayor said he understood the "impulse to find another location for the mosque" but a compromise won't end the debate.
"The question will then become how big should the no-mosque zone around the World Trade Center be," Bloomberg said. "There is already a mosque four blocks away. Should it, too, be moved?"
Sharif el-Gamal, the mosque site's developer, and Daisy Khan, a co-founder of the group planning the mosque, were also at the dinner attended by about 100 people, including members of the Muslim community and city officials such as police Commissioner Raymond Kelly.
After Bloomberg spoke, el-Gamal said he was "very honored and blessed" to be an American and a New Yorker.
"Mayor Bloomberg's speech embodied the values and the mores that we as Muslim Americans live and cherish," el-Gamal said.
Khan said Bloomberg "delivered a passionate speech in defense of our deep American values."
Meanwhile, the heated rhetoric surrounding the proposal for an Islamic community center and mosque two blocks from the World Trade Center site drew concern from Archbishop Timothy Dolan, who said Tuesday the tense climate could put New Yorkers in danger of losing their sense of tolerance and unity, values they embraced in the days after the 2001 attacks.
"We're just a little bit apprehensive that those noble values may be a bit at risk in the way this conversation and debate about the site of the mosque is taking place," Dolan, the leader of the area's Roman Catholics, said after a meeting with Gov. David Paterson about the issue.
A national survey underscored the complex views of Americans toward the mosque project, with 51 percent agreeing with opponents of the Muslim center, while 34 percent said they supported it. The poll of 1,003 randomly chosen adults was conducted by the nonpartisan Pew Research Center and showed that a majority, 62 percent, also said Muslims have equal rights to build houses of worship.
While supporters of the mosque say religious freedom should be protected, opponents say the mosque should be moved farther away from where Islamic extremists destroyed the World Trade Center and killed nearly 2,800 people on Sept. 11, 2001.
Dolan said both sides of the debate have legitimate stances.
"I sure don't have strong feelings on where the mosque should ultimately be," he said during a brief news conference after meeting with the governor.
They spoke about how religion can be brought to bear on the debate over the proposal in an effort to encourage reconciliation and community, rather than divisiveness, Dolan said, and expressed willingness to be part of the dialogue if asked.
New York Assembly Speaker Sheldon Silver, who represents the lower Manhattan district where ground zero is, suggested Tuesday that Islamic leaders should move the proposed mosque. Paterson has made the same point.
Organizers have the right to build the center at a building two blocks north of ground zero but should be open to compromise, Silver said.
"In the spirit of living with others, they should be cognizant of the feelings of others and try to find a location that doesn't engender the deep feelings the currently exist about this site," Silver said.
Paterson has yet to meet with anyone from The Cordoba Initiative, the project's organizer.
Its co-founder, Imam Feisal Abdul Rauf, is on a Mideast trip funded by the U.S. Department of State. He alluded to the controversy at a dinner Sunday night for student leaders at the U.S. ambassador's residence in Manama, Bahrain.
"The fact we are getting this kind of attention is a sign of success," he said. "It is my hope that people will understand more. ... This is something we are doing for your generation."
Rauf also thanked President Barack Obama, who has said Muslims have the right to practice their religion and build the Islamic center in lower Manhattan. The president later said he wasn't endorsing the specifics of the plan.
The White House said Tuesday that Obama would have no further comment on the issue and that the administration will not get involved in talks about relocating the facility. Republicans have vowed to make Obama's supportive comments a campaign issue in this fall's midterm elections.