'The danger is not over, ' said interior minister Fernando Grande-Markaska.
"From then, until the end of the week, it's going to be very hard to get about", he told Sexta television.
The blizzard also yielded unusual images for many Madrilenos, including a few fearless people heading out with their ski gear on the Spanish capital's main commercial avenue and in the central Puerta del Sol square, and even a dog sled that was seen on videos widely circulated on social media.
Madrid's global airport began gradually resuming operations on Sunday afternoon, having cancelled all flights on Friday.
The capital's Barajas airport was shut from Friday night, while nationwide, more than 650 roads were blocked.
Storm Filomena moved Sunday to the regions of Catalonia and Aragon in the northeast of the country, affected by less snowfall than in the center of the country the day before.
"The commitment is to guarantee the supply of health, vaccines and food".
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Renfe, the state-owned railway company, has also suspended all train services within the capital region as well as all medium and long-distance trains that have Madrid as their point of departure or final destination. Transit authorities called on people to stay indoors and avoid non-essential travel.
Traffic on almost 700 major routes was still disrupted Sunday, while rail travel to and from Madrid was resuming gradually except along the northeastern corridor including Barcelona, the government said.
Neighbours in Bustarviejo, located outside of Madrid, gather for drinks in the middle of the street.
Schools and universities are closed until Wednesday, Madrid regional authorities said.
Atletico Madrid's football game against Athletic Bilbao, scheduled to kick off on Saturday, was postponed, La Liga said in a statement. Many of them decided to make the most of this "emergency situation", as videos on social media show people having snowball fights, as well as skiing and sliding through the streets.
Lucia Valles, a coach for a Madrid-based ski club who usually has to travel to faraway mountains with her clients, was thrilled to see the white layers of snow accumulating literally at her doorstep.
"I never imagined this, it has been a gift", the 23-year-old said.