President Pedro Castillo expressed his condolences to the families of the firefighters in a tweet.
Flight LA2213 was taking off from Lima’s main airport en route to the Peruvian city of Juliaca.
Videos on social media showed smoke coming from a large plane on the runway.
LATAM Airlines said it lamented the death of the firefighters and would provide flexibility to reschedule flights to affected passengers at no extra cost.
But it said it did not know why the firetruck was on the runway.
“No emergency was reported on the flight It was a flight that was in optimal conditions to take off, it had authorisation to take off and it encountered a truck on the runway and we don’t know what the truck was doing there,” said Manuel van Oordt, general manager of LATAM Airlines Peru. “We have to investigate and establish why it was there.”
The Prosecutor’s Office in Callao, where the airport is located, said an investigation into the cause of the accident had been opened.
According to the fire department, the incident was registered at 3:25 p.m. and four rescue units were mobilised.
Aviation authorities said operations at Jorge Chávez International Airport were suspended until 1pm local time Saturday. Flights would be direct to other airports in the meantime.