Bill Gault, president of Local 22, said city officials were being "deceitful" in claiming the action would not affect public safety.
But Fire Commissioner Loyd Ayers said in a statement earlier "Rest assured that we have not closed any firehouses nor did we lay off any of our firefighters and the department will continue to respond to your call and tend to any and every emergency that may arise in an urgent and timely manner."
Gault denied the union's opposition was prompted by the loss of overtime, the main source of the projected $3.8 million in savings.
He said the department created its overtime problem by not hiring more firefighters.
Mayor Nutter last month balanced the city budget by cutting $47 million in spending, including the Fire Department's savings.
Around the nation, cities that are struggling financially have resorted to brownouts, including Los Angeles, San Diego, Cincinnati, Milwaukee, and Sacramento.
A brownout in San Diego might have contributed to the choking death of a 2-year-old boy last month, news organizations there reported. Firefighters at a station one block from the boy's home were responding to a call that would have been handled by another station that was scheduled for a brownout that day.
Of the Philadelphia department's 56 companies, only 23 will be part of the rolling brownouts, Ayers said last week.
Though seven companies were closed permanently last year, the city experienced the fewest number of fire deaths since the 1950s, when such records were first kept.
The department has a 10-hour day shift and a 14-hour night tour, and three companies will be closed during each shift.
Two other companies were closed during the day tour Monday: Engine 34 at 1301 N. 28th St., and Engine 38 at 4960 Longshore Ave.
Engine 34 will be reactivated Monday night. Engine 38 will remain closed and its personnel will be reassigned until a new firehouse is built. That could take up to two years. The company had to move to make way for expanding I-95.
Engine 38's ongoing closing counts as one company per shift, so other companies will rotate through the two other slots each tour.
Throughout August, two Center City ladder companies will be closed on alternate nights: Ladder 9 at 21st and Market Streets, and Ladder 23 in Chinatown.
Ten engine companies will make up the day rotation in August. Engines 57 and 34, closed Monday, will be closed again Saturday.
"It's a shell game," Gault said in a statement on the union's website. "One day you're protected, the next you're not. If you live in Center City or Chinatown you are protected during the day but not at night. This plan makes no sense."
Ayers said that several factors were considered when determining which fire companies to close and when: workload, the area covered, proximity to other companies that were closed last year, the capability of surrounding companies to respond.
Contact staff writer Robert Moran at 215-854-5983 or firstname.lastname@example.org.