At least four deaths had been confirmed late Friday, The New York Times reported. Many villages were without communications and cut off by flooded roads. The actual number of people killed by the storm was expected to be higher.
More than 18,000 people went to evacuation centers in Ubay, Jagna, Talibon and Loon in Bohol, inquirer.net reported in its Saturday edition. More than 8,700 families sought shelter in Western Visayas; about 8,000 went to shelters in Southern Leyte; more than 1,500 in the towns of Tarangnan and Matuguinao in Samar province; 6,000 in the province of Cebu; and 7,400 in the cities of Cebu and Lapu-Lapu, the report said.
A shelter was set up in a cave formerly used as headquarters by a rebel leader, inquirer.net said.
Thirty-three families were sheltering in the Popog cave, not far from the village of Marcelo.
Patricio Salingay, 62, was at the shelter with his family when he told the website the cave has been a typhoon evacuation center since he was a boy.
The storm's high speed lessened its impact. Haiyan, known in the Philippines as Yolanda, moved about twice as fast as last year's Typhoon Bopha, which caused 1,000 deaths.
Slower-moving storms dump more rain, increasing flooding and mudslides.
"Fortunately, this moved like a Porsche," Michael Padua, a senior typhoon specialist at Weather Philippines, a commercial forecasting company, told the Times.
Experts said the country had prepared for Haiyan. The National Disaster and Risk Management Council said about 700,000 people had heeded the words of President Benigno S. Aquino III and evacuated before the storm hit.
Haiyan flooded streets, flattened trees, caused power outages and stranded travelers.
Haiyan made landfall about 4:30 a.m. Friday on the island of Samar and moved on to four other islands. Forecasters said its track is likely to take it to Vietnam.
The Times said many meteorologists in the Philippines disputed reports from outside experts that Haiyan is the most powerful storm to hit the country since the advent of scientific meteorology.
Those estimates, which said Haiyan had top sustained winds of as high as 195 mph, were based on the study of satellite images.
"Some of the reports of wind speeds were exaggerated," Rene Paciente, a government meteorologist, told the Times.
Maryann Zamora, a field communications specialist for the World Vision charity, told CNN by telephone from Cebu Island her organization "has been working through so many disasters, so many typhoons -- but this is quite different ... this is the strongest I ever felt so far."
Gov. Roger Mercado of Southern Leyte province in Eastern Visayas near the storm's path said roads were impassable because of downed trees.
"We don't know the extent of the damage," Mercado said. "We are trying to estimate this. We are prepared, but this is really a wallop."
Haiyan, which has the strength of a Category 5 hurricane in the Atlantic Ocean, was so large at one point, its clouds were affecting two-thirds of the country, which spans more than 1,150 miles, CNN said.
Philippine authorities said there were 109 storm evacuation centers in 22 provinces.
Sea travel was suspended, stranding more than 3,000 travelers in ports, officials said.
CNN said some of the people most vulnerable to the storm were those living in temporary shelters on the island of Bohol, which experienced heavy wind and rain but wasn't in Haiyan's direct path. The island was hit by a 7.1-magnitude earthquake last month that killed at least 222 people, injured nearly 1,000 and displaced about 350,000.