Cars and houses remain submerged after tonnes of mud and stones swept down the mountainous island and into the regional capital, Funchal.
At least 40 people have died in the flash flooding, and around 100 people have been taken to hospital.
Portugal has rushed medical teams, rescuers, divers and relief supplies to the tourist island, warning that more bodies would be found in the mud that filled houses and swept people off their feet as they tried to escape.
The main airport is closed, power and telephone lines have been torn down and authorities have told people not to risk their lives by venturing out.
People who left their homes in Funchal struggled to keep their feet in torrents of muddy water that poured down the hillsides and out of alleys.
The flash floods destroyed houses and bridges, particularly around Funchal and the Ribeira Brava region, both on the south of the island.
The Portuguese naval frigate Corte-Real set off from Lisbon for Madeira late on Saturday with helicopters, a medical team and relief supplies, a military statement said.
Two helicopters and two C-130 Hercules transport aircraft were also en route.
Eighty-nine police and firefighters were to leave Lisbon for Funchal on Sunday.
The head of the regional government held talks late on Saturday with European Commission president Jose Manuel Barroso in a bid to get European Union aid.
Portugal’s president Anibal Cavaco Silva, said King Juan Carlos of Spain had promised any aid needed.
The strong winds and heavy rain caused flooding and landslides, particularly in the south of Madeira, which is 900 kilometres south-west of the Portuguese mainland and 500 kilometres from the African coast.
Winds exceeding 100 kilometres per hour, high seas and blocked roads made rescue attempts even more difficult for emergency services, though weather experts said the worst of the storms was over.
Electricity and telephone networks were severed in many areas.
In Funchal, one elderly woman died when the roof of her house caved in and two others were crushed by a crane, local media reported. Several residents were evacuated from their homes.
“I am very worried because I only know what I see from my window,” Funchal resident Margarida Freitas Vieira told the Lusa news agency describing the disaster. “The sea is all brown, there are enormous waves.”
By late Saturday, the town had no electricity and phone lines were also down.
Madeira authorities advised people to stay at home and appealed for doctors and other medical staff to come in to help relieve the pressure on overworked hospital staff.
Officials evacuated the lower part of Funchal, which has 100,000 of the 250,000 who live on Madeira.
“It had been raining since dawn and our hotel was evacuated as it is near a river in the city centre,” Aymeric Payan, a French hotel employee in Funchal, said.
Portuguese media said the storms were the deadliest in Madeira since October 1993, when eight people died.
Prime minister Jose Socrates expressed shock at the deaths and promised support for the islanders.