Almost 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.
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At least 19 people have been killed in forest fires in central Portugal.
"I am shocked with this death toll". "I never thought it would come to this side", she said.
The source of the fire, which broke out at around 2pm local time on Saturday, is so far unknown, but will be determined "in due course", PM Costa added.
He said authorities are working to identify the victims, and Spanish rescuers are to help efforts to put out the fires.
A firefighter helps a woman during a forest fire in Pedrogao Grande.
Dozens of others are said to have been injured, with four firefighters reported to be among those most seriously hurt.
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"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.
Jorge Gomes, Secretary of State for the Internal Affairs, said that 30 of those who died were found trapped inside their cars, with another 17 next to their vehicles.
Gomes also said 18 of the 59 injured have been taken to the hospital.
The blaze on Saturday hit the mountainous area of Pedrogao Grande, 200 km southeast of Lisbon, amid an intense heat wave and strong winds that fanned the fire later in the day.
Mr Costa said that they are witnessing a bad tragedy.
Overnight, about 60 forest fires were ignited across the country.
"The priority now is to save those people who could still be in danger". "The Portuguese people have our solidarity, support and affection", Spain President Mariano Rajoy Brey wrote on Twitter.
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