Mr. de Blasio and Mr. Lhota describe themselves as guardians of religious freedom who respect Mr. Bloomberg’s efforts to maintain the separation of church and state but believe he has ignored the needs of religious communities. And Mr. Lhota suggested Mr. Bloomberg had sometimes encroached on the rights of New Yorkers of faith.

“Government should not interfere with religious practice,” Mr. Lhota said in an interview. “We have a government here in the city that has attempted that on a number of occasions.”

Mr. de Blasio said Mr. Bloomberg had governed as if he had a “blind spot” to faith-based groups. “I don’t think the mayor really understands how crucial it is to protecting the fabric of the city,” Mr. de Blasio said in an interview.

Mr. Bloomberg, who is Jewish, has repeatedly expressed a desire to keep religion and government separate, an attitude common among American Jews. “This business of bringing religion into everything is just bad because if you really believe in religion you should be the person out there championing separation of church and state,” he told a biographer, Joyce Purnick, a former reporter and editor for The New York Times. And the mayor’s spokesman, Marc LaVorgna, said last week, “His actions are guided by his belief that the Constitution and Supreme Court rulings aren’t just pieces of paper.” However, Mr. LaVorgna also pointed to the mayor’s defense of the proposed mosque, despite a public uproar, saying, “The mayor stood up and forcefully defended the bedrock principle of religious freedom while nearly every other politician in this city hid for cover.”

Nonetheless, the changes proposed by Mr. de Blasio and Mr. Lhota would represent a shift in tone for New York, a city home to an array of religions, but often synonymous with secularism.

“There’s an openness that you did not see with Bloomberg,” said James R. Kelly, a professor emeritus of sociology at Fordham University. “They are saying, ‘I really am reaching out. I am more inclusive.’ ”

Mr. de Blasio and Mr. Lhota both come from families with ties to the Roman Catholic Church.

Mr. de Blasio, who does not attend church, was raised in a household that did not follow any faith. His father was skeptical of organized religion, and his mother, the daughter of Italian immigrants, left the Catholic Church as a young woman.