City Councilman Ben Kallos, who represents the Upper East Side, has led the opposition. “The overall narrative everyone is giving is like, ‘Oh, this is all about NIMBY, this is about a nonprofit and this is about shadows,’” he said. “At the end of the day, this is about an 11-story tower that is somehow 233 feet tall that is a glorified office space for wealthy people.”

Mr. Kallos noted that the Blood Center, under current zoning, could construct a building on the site exceeding 200,000 square feet without additional city approval, more than the amount of space the center plans to occupy in the proposed tower.