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.
