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.
The power outrage caused chaos at airports across the country (Image: Getty)
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 warned 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.
Spain's rail network was brought to a halt as a result of the power failure, causing chaos for passengers and commuters.
The Transport Minister Oscar Puente said it is not likely that medium and long-distance trains will resume normal service today.
He added that the intention is to resume shorter distance commuter services as soon as the electricity supply has been restored.
Work is also under way to rescue those trapped on stranded services. The aim is to resume full service on Tuesday if the electricity supply is restored today.
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Puente also noted that air traffic is currently operating at "80% of its capacity". The 20% reduction is due to security precautions relating to telecommunications.
Earlier on Monday, Portugal's TAP Air urged passengers intending to fly from Lisbon to avoid the city's airport until further notice.
In a statement on Facebook, the airline company wrote: "Due to the power cut in several European countries, the operation of airports is temporarily very limited.
"TAP requests that you do not go to the airport until further information."
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