The weather improved on Sunday following Saturday's rains, making it easier for rescue workers.
But regional social services spokesman Francisco Ramos said there were "great difficulties" in communications and that the death toll "will likely increase, given the circumstances of this flood".
Three remote areas in the south of the island have been cut off. Officials fear more bodies may be found there.
The Portuguese cabinet is due to discuss the crisis in an extraordinary meeting on Monday, and expected to announce three days of national mourning.
Prime Minister Jose Socrates, who is on the island, said he was "profoundly shocked" by the severity of the floods, and promised that his government would help Madeira recover as quickly as possible.
The military has sent specialist rescue and medical teams to the island. Construction companies on the island have lent equipment to clear the streets.
Autonomous region of Portugal with population of around 250,000
Lies just over 480km (300 miles) from West African coast
The European continent is more than 900km away
The Spanish government has offered its help with the rescue effort.
Madeira, located about 900km (560miles) from the Portuguese mainland, is popular with foreign tourists.
The Foreign Office in London said a British national had died in the floods, and that a small number of Britons were in hospital on Madeira.
The world's most famous Madeiran, Real Madrid football star Cristiano Ronaldo, said he was "shocked and dismayed" by the floods.
"Nobody can remain indifferent to the disaster," he said. "I want to express my willingness to, as far as I can, help agencies and authorities to overcome the effects of this devastation."
The BBC Weather Centre says the severe weather was due to a low pressure system, and that while Madeira can expect further rain with heavy downpours on Sunday, there is no danger of a repeat of the flash floods.
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