The Buildings Department did an about-face on the fate of fire-ravaged St. Sava’s Cathedral a week after telling church officials the West 26th Street edifice had to be demolished.

“We recommend that the remaining building components be demolished as soon as possible,” read a May 27 letter signed by inspecting engineer Nathaniel Smith.

The Post reported on the imminent demolition Tuesday after it was announced by the church, and a Buildings Department spokesman said, “There has been a preliminary determination that the structure is compromised.”

A day later, the same spokesman told The New York Times that the 161-year-old structure was safe.

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

Church officials were left scratching their heads. “There have been many sleepless nights since the report was issued,” said a source.

Schnell said he had no evidence that a Buildings official told church leaders the structure would be demolished.