The government declared three days of national mourning as expressions of sympathy and offers of assistance poured in from leaders across the world, including Pope Francis, French president Emmanuel Macron and German chancellor Angela Merkel.
Portugal was hit by a series of fires past year which devastated more than 1000 square kilometres of the mainland.
Numerous victims died as they tried to flee the fire northeast of Lisbon in their cars.
Police chief Almeida Rodrigues blamed dry thunderstorms, ruling out arson and saying a tree had been struck by lightning.
Gomes says 54 people have also been injured, 5 of them seriously, including four firefighters and a minor.
The death toll was earlier on Sunday reported at 62 people, but Portugal Prime Minister Antonio Costa later reduced it to 61 because authorities allegedly counted one victim twice.
At least 30 people died in vehicles, with more bodies found near cars on the side of a road and others in rural areas near Pedrogao Grande, Secretary of State for Internal Administration Jorge Gomes said in comments broadcast Sunday by RTP. The ceremony took place before the teams' match Sunday at the Confederations Cup tournament.
FIFA President Gianni Infantino, attending the match in Russian Federation, also offered his condolences. He says "we want to send a big hug to everyone in Portugal for what they are going through, which is absolutely awful".
President Marcelo Rebelo de Sousa, who comforted survivors at the scene, said a rare combination of high temperatures, strong winds and zero humidity appeared to have contributed to the rapid spread and the extent of the fire, with different fronts extending for several kilometres. The European Commission said on Sunday that France and Spain have sent firefighting aircraft. Spanish Prime Minister Mariano Rajoy tweeted that he was "overwhelmed by the tragedy at Pedrogao Grande".
The prime minister said the emergency services acted as fast as they could but acknowledged that some of the efforts like alerting the population might have been hindered because the blaze had ruined phone lines and communications towers.
Authorities had previously said that temperatures which have soared to 40C in recent days might have played a part in the inferno, centred about 95 miles north-east of the capital Lisbon. Government officials said an assessment will be made of the cause.
Portuguese Republican National Guard soldiers battle with a forest fire in Capela Sao Neitel, Alvaiazere, central Portugal, on June 18 2017.