More than 5,300 firefighters with more than 1,600 vehicles were still battling the fires through dense pine and eucalyptus forests Monday.
Initially, officials put the death toll at six and no one was immediately available to confirm the rising death toll.
In neighbouring Spain, more wildfires killed at least four people and prompted the evacuation of thousands in the north-west region of Galicia, as the remnants of winds from Hurricane Ophelia fanned the flames along Iberia's Atlantic coast. An independent investigation into those fires found last week that authorities failed to evacuate villages on time.
Spanish Prime Minister Marian Rajoy, who is from Galicia, traveled to the region Monday to visit an emergency response center.
"We went through absolute hell, it was disgusting".
Five wildfires were raging near Vigo, Galicia's biggest city, forcing authorities to close schools, roads and factories and shelter people forced to leave their homes in sports centres and hotels.
The 524 registered outbreaks of fire in Portugal, by far the most since 2006, were caused by "higher than average temperatures for the season and the cumulative effect of drought", Gaspar said.
She said 56 people were injured, 16 of them seriously, and nine people were reported missing in the blazes that broke out over the weekend.
Spanish TV pictures showed people trying to fight fires with buckets of water. "There was fire everywhere", a resident of the town of Penacova, near Lousa. told RTP television. He said "Galicia is fed up" with being attacked by arsonists who make the most of weather conditions, adding that some purposely tried to cause most damage by targeting urban areas.
The 36 deaths, which were confirmed by Portugal's national civil protection agency and included a one-month-old baby, come four months after 64 people were killed in the deadliest fire in the country's history in June.