He said the government was making temporary shelters available for hundreds of people left homeless in the flooding.
Describing the situation on the island to Al Jazeera over phone, Ana Basilio, a reporter for Lusa News Agency, said: "When it all happened, we couldnt see anything, we couldnt walk.
"People in the market had to be evacuated while shopping. People with cars couldn't move in the roads. Communications were all off, so people couldn't reach their families.
"We are a mountain island, and water just came down the river carrying everything in its way. There were cars, fridges and cupboards and even people. And we couldn't do anything.
"A fireman who tried to [rescue] a lady was carried by it too.
"This morning [Saturday] we will see the destruction because at night it was really hard [to assess].
"There are a lot of people missing. We don't know if they are alive or dead. We will know this morning when the lights come on."
Jose Socrates, the Portuguese prime minister, has expressed "profound shock" at the disaster and promised support for those affected.
"I am absolutely saddened and shocked with the images, with the consequences of this calamity," he said, as he prepared to travel to Madeira to assess the damage.
Television footage showed powerful streams of water and mud flooding the streets of Funchal, dragging and overturning cars and destroying trees.
"We have no memory of something like this ... with so many people dead"
Rachel Goncalves, a journalist in Funchal
It was not immediately clear whether any tourists were among the victims.
Rachel Goncalves, a journalist in Funchal, described the scene as "chaotic".
"We have no memory of something like this ... with so many people dead," she told Al Jazeera.
"There are dramatic stories of a man who saw his family swept away by the waters in Funchal. It's a very dramatic situation and this is only one such story, there are more," she said.
Portuguese authorities have promised to organise aid for the autonomous region, and the country's government has said it is considering asking the European Union for help with the crisis.
Jardim, Madeira's regional leader, spoke to Jose Manuel Barroso, the Portuguese European Commission president on Saturday, to appeal for emergency aid from the European bloc.
Officials said they are also discussing whether to declare a state of emergency on the island.