The proposed Islamic community center and mosque in Lower Manhattan got its strongest vote of confidence yet from major Muslim leaders on Monday, after months of behind-the-scenes grumbling that they were not properly consulted on the project, and a day’s worth of intense and painful conversations at a hotel near Kennedy International Airport. Leaders of local and national groups gathered at the site of the planned center, two blocks from ground zero, and declared not only that the planners had a constitutional right to build it, but also that they would help the project move forward in the face of heated opposition. They insisted that, as a matter of principle, the center should not budge from its planned site. But the unity news conference followed a two-hour meeting on Sunday in which the leaders asked tough questions of Sharif el-Gamal, 37, the real estate developer spearheading the project. Mr. Gamal fully embraced Islam only as an adult and was meeting many of the nation’s Muslim communal leaders for the first time. In interviews on Monday afternoon, many of the participants said that Mr. Gamal had satisfied most of the concerns that American Muslims had about the project: that it was elitist and had not been sensitively planned or promoted. According to people at the meeting and other members of their organizations, the developer apologized for not consulting more with leaders ahead of time and said that he had not realized how strong the opposition would be. He also addressed concerns that the center would be only for “Manhattan elites” who have embraced interfaith dialogues led by the imam involved in the project, Feisal Abdul Rauf, or can afford its potentially expensive amenities like swimming pools and gym memberships. Aisha al-Adawiya, who founded Women in Islam, based in Harlem, said participants stressed that the center should be accessible to poorer Muslims and offer programming that addressed their interests and needs.