“We don’t see that it’s impossible to stabilize the structure and preserve what remains while ensuring that public safety is not compromised,” Alexander Schnell, a spokesman for the agency, said.

On Sunday, the cathedral posted a bulletin on its website that read, “As the remaining church walls are determined to be unstable during inclement weather and winds exceeding 25 m.p.h., the D.O.B. has, based on engineering recommendation, reached a decision to demolish the church.”

The New York Post picked up the report on Tuesday, saying the cathedral “will be demolished by order of the city.”

However, Mr. Schnell said, “We have not reached that decision.”

The brownstone Gothic Revival church was designed by Richard Upjohn and completed in 1855 as a chapel of ease for Trinity Church in Lower Manhattan. It was designated an official city landmark in 1968.

Because of its landmark status, an extra layer of scrutiny would apply to any request by the cathedral for permission to demolish the building under an emergency declaration from the buildings agency.