Emergency service workers were battling 156 fires across the country on Sunday, Prime Minister Costa said, adding that most of the victims had died in just one of them.
Interior Ministry official Jorge Gomes said 60 people died from the flames and suffocating smoke, while another two people perished in a traffic accident related to the fires.
Forest fires are common in the the Iberian peninsula during the summer months, but today's example is particularly extreme.
Leaders from around the world have expressed their condolences and the government has declared three days of national mourning.
As a result, a Spanish firefighting aircraft was already assisting on Sunday morning and another one was expected to arrive later in the day. Fourteen of the injured were in serious condition, RTP said.
The loss of life due to a forest fire is the biggest in memory in Portugal.
"This is a region that has had fires because of its forests, but we can not remember a tragedy of these proportions", Valdemar Alves, the mayor of Pedrógão Grande, was quoted as saying by the Associated Press agency.
Officials describe as the "greatest wildfire tragedy of recent years".
"I am completely stunned by the number of deaths".
The European Commission says it is working with EU member states to respond to the call for assistance issued overnight by Portuguese authorities in order to fight the forest fire in central Portugal that has claimed 57 lives so far. In August of a year ago, the island of Madeira was devastated by a fire that killed three people and more than a thousand had to be evacuated from their homes.
On Sunday, Costa also tweeted his "deepest regret for the victims. and a word of encouragement and strength for all who help combat this scourge".
France has offered three firefighting planes, while Spain has already sent two water-bombing aircraft to help tackle the fires.
Investigators believe the fire was sparked by a lightning strike during a "dry thunderstorm".
Pope Francis has led thousands of people in a moment of silent prayer for the victims of the Portugal fire.
Mariano Rajoy has tweeted that he is "overwhelmed by the tragedy at Pedrogao Grande".
"I express my closeness with the dear Portuguese people for the devastating fire that is affecting the forests around Pedrogao Grande, causing many deaths and injuries". Portuguese officials are visibly shocked.