Nearly 600 firefighters and 160 vehicles were dispatched late Saturday to tackle the blaze, which broke out in the afternoon in the municipality of Pedrogao Grande, about 50 kilometres (30 miles) from Coimbra, before spreading fast across several fronts.
"Unfortunately, this seems to be the greatest tragedy we have seen in recent years in terms of forest fires," a visibly moved Prime Minister Antonio Costa said.
"The number of fatalities could still rise," he said at the Civil Protection headquarters near Lisbon.
"The priority now is to save those people who could still be in danger."
The European Union said it would provide firefighting planes following a request from Lisbon.
"France has offered three planes through the EU Civil Protection Mechanism and they will be quickly sent to assist the local emergency efforts," EU Commissioner for Humanitarian Aid and Crisis Management Christos Stylianides said.
Portugal was sweltering under a severe heatwave across the weekend, with temperatures exceeding 40 degrees Celsius (104 degrees Fahrenheit) in several regions.
Some 60 forest fires broke out across the country during the night, with around 1,700 firefighters battling to put them out.
Secretary of State for the Interior Jorge Gomes said 57 people burned to death, mostly trapped in their cars engulfed by flames in the Leiria region. At least 59 were injured.
"The fire is still raging on four fronts," he said, of which two were spreading "violently".
"It is difficult to say if they were fleeing the flames or were taken by surprise," Gomes said, speaking of the dead.
- National mourning -
Dry thunderstorms were thought to have been the cause of the fatal blaze, according to the prime minister.
"There are people who arrived saying they didn't want to die in their homes," Ricardo Tristao told AFP.
Officials were not immediately able to comment on the extent of the damage.
Spain dispatched two water-bombing planes on Sunday morning to aid the Portuguese fire service on the ground, Costa said.
He added a period of national mourning would be announced shortly.
"My thoughts are with the victims in Portugal," EU commission head Jean-Claude Juncker tweeted. "I commend the bravery of the firefighters. EU civil protection mechanism activated & will help."
President Marcelo Rebelo went to the Leiria region to meet families of the victims, "sharing their pain in the name of all the Portuguese people," he said.
Firefighters did "all they could" when faced with the blaze, he added.
Dozens of people who fled their homes were taken in by residents of the nearby municipality of Ansiao.
"There are people who arrived saying they didn't want to die in their homes, which were surrounded by flames," Ansiao resident Ricardo Tristao told reporters.
Portugal was hit by a series of fires last year which devastated more than 100,000 hectares (1,000 square kilometres) of the mainland.
Fires on the tourist island of Madeira in August killed three people, while over the course of 2016 around 40 homes were destroyed and 5,400 hectares of land burned.