Although Kalmaegi, locally named Tino, has weakened since making landfall early on Tuesday, it continued to lash the country with winds of 130km/h and gusts of 180km/h as it swept across the Visayas islands headed for northern Palawan and towards the South China Sea.
The number of people killed climbed to 40 late on Tuesday, all but one of those in the central province of Cebu, provincial information officer Ainjeliz Orong said.
One person was reported dead on the nearby island of Bohol, according to the disaster agency.
Asked why the sudden jump in casualties, Orong said rescue operations were underway and information had just started to come through.
"Search and rescue efforts continue and there are missing and unaccounted individuals," Orong said in a phone message, adding the deaths were due to drowning and falling debris.
Tens of thousands of residents were relocated across the Visayas region, including parts of southern Luzon and northern Mindanao, authorities said.Â
The typhoon was expected to leave the Philippines late on Wednesday or early Thursday.
Floods in Cebu City had subsided late on Tuesday but power was still out in many places and telecommunications services were intermittent, a Reuters journalist in Cebu said.
Photos and videos from the Philippine Red Cross showed rescue workers wading through knee-deep floodwaters in Cebu City, using boats to reach stranded residents.
In Liloan town, on the northern outskirts of the city, homes were submerged, with only rooftops and top floors visible.
Similar scenes from other parts of Cebu City, with vehicles and streets under water, circulated on social media.
State weather agency PAGASA said the combination of Kalmaegi and a shear line had brought heavy rains and strong winds across the Visayas and nearby areas.
More than 180 flights to and from the affected areas were cancelled on Tuesday, while those at sea were advised to head to the nearest safe harbour immediately and to stay in port.
PAGASA had earlier warned of a high risk of "life-threatening and damaging storm surges" that could reach more than three metres high along coastal and low-lying communities in the central Philippines, including parts of Mindanao.
The Vietnamese government also said on Tuesday that it was preparing for the worst-case scenario as it braced for Kalmaegi.
The typhoon is forecast to make landfall on Thursday night in Vietnam's central regions, which have already suffered heavy floods that killed at least 40 people and left six others missing over the past week.
"This is a very strong typhoon, which continues to strengthen after entering the East Sea," the government said in a statement, referring to the South China Sea.
