Authorities have confirmed the flash floods killed at least 42 people.
Some of the missing may never be found - officials suspect many may have been swept out to sea when torrents poured down the Atlantic island's steep slopes. Navy divers have joined in search operations Tuesday.
The number of missing was raised from four earlier in the day after local people contacted authorities, said Conceicao Estudante, the regional head of tourism and transport.
"The situation is totally different from this morning," Estudante told reporters. "There are now 32 missing people, all of them identified by name."
Authorities are checking whether bodies might be trapped in piles of debris or in submerged underground parking lots.
Rescue teams used sniffer dogs flown in from Lisbon (Portugal's capital) to scour debris, and dug cars
out of mounds of sludge to see if anyone was inside.
Rescue workers in Funchal removed the body of a man who had been encased in mud in his car.
"We are sifting through the debris," the president of the island's regional government, Alberto Joao Jardim, said in an interview with public broadcaster Radiotelevisao Portuguesa. "My fear is that the missing will be recorded as lives that were lost."
Officials said all the 42 confirmed dead were either from Funchal, the island's capital, or Ribeira Brava, a village at the foot of a valley about 10 miles from Funchal. The two oceanside communities bore the brunt of the mud and rock slides after a storm Saturday dumped the rainfall of a normal month in just eight hours.
The Portuguese government announced three days of mourning for the victims of Madeira's worst disaster in living memory.
Crews in Funchal pumped water out of a shopping mall's underground parking lot, where they feared they might find more bodies. The lot's two levels were submerged in the freak deluge.
A nearby street was littered with earth-filled cars and stacks of catalogues used as stepping stones through the mud.
Anais Fernandes, a store clerk, described seeing the water knock out a bridge.
"People were crossing, and you started to hear screams," she told Associated Press Television News. "Everyone was running together. It was horrible."
Emergency crews used bulldozers and front-loaders to remove tons of caked mud, boulders and 대구출장샵
fallen trees from drains and rivers, hoping to speed water runoff and prevent further flooding.
"We've been going flat-out for 48 hours and we'll keep going till the job's done," Funchal Mayor Miguel Albuquerque said.
Local residents were jittery as showers swept in, dumping more water on sodden hillsides.
Estudante, the regional official, said 13 victims still had not been identified. She asked family members to go to a makeshift morgue at Funchal airport.
Seven members of an eight-member family died when their hillside home was swept away, Radiotelevisao Portuguesa reported.
Officials said 18 of 151 people admitted to Funchal's main hospital were still being treated. Some 150 people were homeless.
Rui Pereira, the Minister for Internal Administration, said in Lisbon that authorities were sending a second batch of aid to the island.
A military transport plane was heading to Madeira with more sniffer-dogs, high-powered pumping equipment and equipment for army sappers to replace collapsed roads and bridges, Pereira said. He said Madeira's financial needs were still being calculated.
Madeira, a popular tourist destination, is the main island of a Portuguese archipelago of the same name in the Atlantic Ocean just over 300 miles off the west coast of Africa.