"We stand for the constitutional right of Muslims, and Americans of all faiths, to build houses of worship anywhere in our nation as allowed by local laws and regulations," the Muslim leaders said in a statement delivered at the site of the proposed Islamic center and mosque, to be called Park51.
They called for a "week of dialogue" on the weekend of Oct. 22-24, during which Muslims would conduct open houses at their places of worship to help ease tensions.
"We ask Muslims to open mosques nationwide to welcome people, to let them understand the Islamic faith and what American Muslim community is," said Nihad Awad, national executive director of the Council on Islamic-American Relations. "We also urge Muslims to visit places of worship in other faith communities."
The Muslim leaders spoke after a daylong summit meeting Sunday at a hotel near Kennedy Airport.
The 20 groups participating in the summit included CAIR and the Islamic Society of North America, the two best-known U.S. Muslim groups, as well as the Islamic Circle of North America and the Muslim Alliance in North America.
Neither the developer of the Islamic center nor its imam attended the news conference. Imam Feisal Abdul Rauf Rauf welcomed the Muslim leaders' support in a statement.
"On a day when American Muslim leaders stand strongly in favor of protecting civil rights, and denouncing bigotry in all forms, it is important to remember that world-wide efforts to foster peace must begin in our home communities," Rauf said.
Park51's proposed location two blocks from the World Trade Center site has upset some relatives of Sept. 11 victims and led to angry demands that it be moved. Critics say the site of mass murder by Islamic extremists is no place for an Islamic institution.
"Ground zero belongs to all Americans," Awad said.
Republicans including Sarah Palin and Newt Gingrich have denounced plans for the mosque, and a Florida pastor threatened to burn copies of the Quran because of it.
The Muslim leaders called on elected officials "to join their colleagues in denouncing and rejecting inflammatory rhetoric that endangers the lives of Muslim Americans."
While the leaders said they supported the mosque, none promised financial backing.
Ihsan Bagby, an associate professor of Islamic studies at the University of Kentucky, said the organizations' support would facilitate fund-raising for the project.
"The summit has underlined the support of the major national Muslim organzations for the Park51 project," Bagby said. "And in doing so they have opened the door for fund-raising in the American Muslim community."
Participants at the news conference refused to answer a question about whether they would denounce Hamas, the militant Palestinian group that that United States considers a terrorist organization.
More one the proposed Islamic Center:
Fact Check: The "Ground Zero Mosque" Debate
NYC Imam: Working on Solution to Defuse "Crisis"
Imam: Moving Cultural Center May be Difficult
Islamic Center Demonstrators Gather on 9/11
Proposed Islamic Center Divides 9/11 Families