While visiting a trade fair in Madrid, the Socialist premier expressed his “solidarity with the families of the 12 people who died” and said the government would spare no effort to locate the four missing “as soon as possible”.
Local authorities had previously reported 11 storm-related deaths since Sunday, when Storm Gloria hit the region bringing strong winds, torrential rains and heavy snow, battering Spain's southern and eastern flanks before moving north.
Gale-force winds and huge waves of up to 14.8 metres (49 feet) high smashed into seafront towns, with dramatic images showing massive flooding that damaged shops, houses and restaurants.
A storm surge swept three kilometres (two miles) inland up the Ebro river delta south of Barcelona, Sanchez said.
“In some places, more rain fell in a single day than is expected in the entire year,” he added.
“This is the seventh major storm which we have experienced since the start of the storm season,” Sanchez said, describing them as “more and more destructive” and noting that Spain was “especially exposed” to the effects of climate change.
His new government on Tuesday declared a “climate emergency” and pledged to unveil a draft bill on transitioning to renewable energy within its first 100 days in office.
Barcelona city hall on Friday said the storm has caused damage worth €12.5 million ($13.8 million) in Spain's second-largest city in its first estimate of the cost of the bad weather.
The city's nine beaches lost an average of 30 percent of their sand due to waves of up to six metres, it said.
The storm caused losses worth €62.6 million to the agriculture sector in the eastern Valencia region alone, according to the ASAJA union of young farmers.
Valencia is Spain's largest producer of oranges, artichokes, pomegranates, plums and other crops.
- VIDEO: Watch Malaga hit by hailstorm as Storm Gloria hits southern Spain
- VIDEO: Watch as seafoam fills streets of Costa Brava resort during Storm Gloria
- VIDEO: Watch as Storm Gloria hits Costa Blanca seaside town of Javea in Spain