A Brooklyn councilman is putting the heat on Mayor Bill de Blasio to reassign a fifth firefighter at all Big Apple engine companies, saying the city should stop cutting corners at the expense of “saving lives.”

Councilman Justin Brannan (D-Brooklyn) told The Post he’ll soon be introducing a resolution “calling on the mayor” to use his powers to reinstate the extra firefighter for runs at all 198 engine companies — reversing a controversial fire department cutback dating back three decades.

The additional staffing would cost the FDNY $100 million yearly, but Brannan and other proponents say bringing back the “fifth man” would help first-responder teams unravel hoses and get water on fires much faster.

“I grew up with so many people who are now [firefighters] and this is all I hear about – especially in the winter months,” said Brannan.

“We’re not looking to reinvent the wheel here. We had the fifth man; we need it back. With an $89 billion [city] budget, who gets to put a price on saving lives?”

Following cuts under the Koch administration in 1988, no more than 60 engine companies at a time have since operated with five firefighters.

In 2011, the FDNY under Mayor Bloomberg removed the fifth firefighter from every company, instead requiring that two engine companies of four firefighters respond to each call.

Critics say that method is flawed because it’s sometimes faster to put out a fire with a team of five, rather than having a team of four show up and then wait for another four-person unit to arrive minutes later to assist with heavy equipment.

Three years ago, the de Blasio administration cut a deal with the city’s firefighters union to reinstate teams of five at 15 of the city’s busiest engine companies. Beginning in February, five other companies will get the added assistance, but the remaining 178 will continue working in teams of four.

Gerard Fitzgerald, president of the Uniformed Firefighters Association, said he backs Brannan’s plan because the current system overworks firefighters with unnecessary calls. He said returning to five-member response teams citywide would free up more units for emergencies.

“We have engine companies that are now doing 6,000 to 7,000 runs a year,” he said. “It’s an insane amount of running.”

However, de Blasio spokeswoman Jaclyn Rothenberg sought to extinguish the flames of Brannan and Fitzgerald’s concerns saying, “The FDNY has operated safely with the vast majority of engine companies staffed with four firefighters for … three decades and, while we continually evaluate our needs, we believe that the current level of staffing is appropriate.”