Cuba's president, Miguel Diaz-Canel, warns all those who may cause unrest. They will be met with powerful measures from the authorities, said the president, dressed in a military uniform, in a television appearance.
Hurricane Oscar has also made landfall from the south over the island and can exacerbate problems with strong winds and heavy rainfall.
When the system went down again, at 17:00 on Sunday evening local time, only smaller parts of the network had been able to be restored.
"Millions of problems"
According to Energy Minister Vicente de la O Levy, Cubans cannot expect the power to return until Monday or Tuesday. The power outage also affects pumps that supply water and internet connections, among other things.
One of the millions affected, Rosa Rodriguez, tells the news agency AP, while queuing for bread, that she has been without electricity for four days.
We have millions of problems and none of them are solved.
80-year-old Elon Foy tells AFP that the situation is crazy.
This shows how vulnerable our power system is. We have no reserves and nothing to keep the country going. We live day by day, according to Foy.
Blaming the USA
Bárbara López, who works with digital content for the internet, says she has barely been able to work in recent days.
This is the worst so far, she says about the outage.
They have really made a mess, we have no power and no mobile connection.
The communist regime blames the USA's sanctions, which it claims have made it harder to obtain spare parts.
Reduced oil deliveries from Venezuela and a general economic downturn after the pandemic are also believed to have contributed.