NEW YORK — American Muslim leaders are starting to coalesce around the concept of building an Islamic center and mosque close to Ground Zero.

Their reason for coming together: The issue has now become a test of their constitutional right to build houses of worship anywhere in the nation.

On Monday, at a press conference outside of Park51, the proposed site of the mosque and community center, national and local Muslim religious leaders said they stood in support “of the building of the mosque in this place.” They said they have had discussions with the property developer about expediting the construction of the controversial facility.

“From the discussion we had with the developer, they are committing to expedite the process, of making sure this project is coherent, has an advisory board from the Muslim community, from the interfaith community, so this project will reflect America in terms of its spirit and its look at the future,” says Zaheer Uddin, executive director of the Islamic Leadership Council in New York.

The group also made clear it views the mosque issue as an important test of American society.

“We are here as religious leaders at a time when there is religious intolerance and bigotry that is prevailing,” said Imam Al-Hajj Talib Abdur-Rashid, deputy amir of the Muslim Alliance in North America. “So we wanted to make clear our unified stance in light of the problems that all Americans are facing because when one group is deprived of their rights, all groups are deprived of their rights.”

The support of the Muslim leaders puts pressure on the Muslim developer of the property, Sharif El-Gamal, to carry through with the mosque building project. For example, Donald Trump, the flamboyant New York developer, wrote Mr. El-Gamal offering $6 million for the property, which was purchased for almost $2 million less.

“Without the support of the Muslim leaders, the construction of the center would have been problematic from the developers’ point of view,” says Susan Lerner, executive director of Common Cause/New York and a supporter of the planned center.

The Muslim leaders’ meeting comes just more than a week after the 9/11 observance at Ground Zero, after which groups either opposed to the construction of the mosque or in favor of it peacefully demonstrated in the streets nearby. The night of Sept. 10, a broad coalition called Neighbors for American Values held a candelit vigil in support of the center.

The construction of the mosque has also become a political battleground. Republicans Sarah Palin and Newt Gingrich, as well as Sen. Harry Reid (D) of Nevada, the majority leader, have come out against the proposed mosque. New York Mayor Michael Bloomberg, an independent, Sen. Orrin Hatch (R) of Utah, and Sen. Richard Durbin (D) of Illinois, the second ranking Democrat, have supported the Cordoba Initiative, as it is sometimes known.

Locally, the Republican candidate for governor, Carl Paladino, has said he will try to take over the project through the right of eminent domain. The Democratic candidate for governor, Attorney General Andrew Cuomo, says the group has a legal right to build the center and says he sees no reason to investigate the donors or funding for the building.

The controversy became even more heated when right before the 9/11 anniversary, a Florida preacher, the Rev. Terry Jones, threatened to burn copies of the Qur’an at his church in Gainesville. Mr. Jones flew to New York after announcing he had an agreement from Imam Feisal Abdul Rauf, who conceived of the Park51 project, to move the mosque.

That announcement proved to be wrong, but Jones suspended the burning of the religious books.

However, the Council on American Islamic Relations reports that some American Muslims are finding burned copies of the Qur’an outside their mosques.

That’s one reason the groups meeting in New York have also called for a national week of dialogue starting around Oct. 22, when mosques will hold open houses. The purpose of the open houses, said the group in a statement, is to help allay tensions caused by Park51 and to “build bridges of understanding that unite and strengthen our nation.”