Half of the deaths were recorded in the southern autonomous region of Bangsamoro, where 10 people were reported missing, the agency said in a bulletin.
Some 48 people were injured, it said. Damage to infrastructure due to heavy rains and strong winds was initially estimated at 384 million pesos ($6.62 million).
President Ferdinand Marcos Jr, who is scheduled on Monday to conduct aerial inspections of submerged villages in Cavite province, near the capital Manila, has expressed shock over the number of deaths particularly in Maguindanao province in the Bangsamoro region.
Nalgae, which has made landfall five times, is this year's second-most deadly cyclone to hit the Philippines, which sees an average of 20 tropical storms annually.
The weather bureau forecast Nalgae would leave the Philippines later on Monday.