Spanish Prime Minister Pedro Sánchez asked the public to use their phones "responsibly" due to pressure on the country's telecoms network.
In his first press conference since the power crisis, he urged people to only use phones for brief calls.
He added that the telecommunications system in Spain was facing a critical moment, with the country still struggling to come to terms with the massive outrage that left millions of people without electricity.
The Prime Minister said hospitals are still functioning and vulnerable people are being treated at their homes.
Sanchez said that power has been restored to some areas in the north and the south of Spain "thanks to help from France and Morocco".
However, he added that the cause of the outrage was still not known and warnd the public against speculation.
Earlier the Portuguese Prime Minister and the and the president of the EU Council said there was currently no evidence to suggest the incident had been caused by a cyber attack.
Portugal's electricity operator also claimed the power cut was caused by "rare" atmospheric phenomenon, related to variations in temperatures.
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