The regional emergency service said a 51-year-old woman and her 61-year-old brother were found dead inside an overturned car that floodwaters washed away in Caudete, about 100 kilometers (60 miles) south of Valencia, Spanish private news agency Europa Press reported.
Officials had initially said the victims were an elderly wife and husband but later corrected themselves.
The Valencia fire department said in a tweet that emergency crews also pulled three people from a river. They included a 57-year-old man and his 33-year-old son, Europa Press reported. A helicopter winched a third person to safety.
Four police were injured in the rescue operation.
The Spanish weather service AEMET classified the region as being "at extreme risk" from torrential downpours. It forecast torrential downpours of up to 90 mm (3 ½ inches) an hour and up to 180 mm (seven inches) over 24 hours.
The storm was passing over the Mediterranean coast regions of Valencia, Alicante and Murcia during Thursday and Friday.
One of the first places to be hit was Ontinyent, a town south of Valencia, where the River Clariano flooded the streets Wednesday night.
Ontinyent mayor Jorge Rodríguez said the town had endured its heaviest rainfall on record, with more than 400 mm (15 inches) by Thursday afternoon.
He said the town would ask the national government to declare a catastrophe in the area, which would entitle local people to emergency aid and long-term financial help to rebuild.
Brown water rushed through streets, washing away cars, and almost reaching the tops of the front doors of houses along the riverbank.
Nearby, sandy-colored water surged over the top of the Pantano de Almansa reservoir and raged down its spillway.
The River Clariano rose nine meters (about 30 feet) in two hours around the Valencia town of Aielo de Malferit and tore apart a 16th-century bridge there, local mayor Juan Rafael Espí told Spanish private news agency Europa Press.
Closed roads and train lines disrupted travel. Trucks, trees and fences blew down, and a mini-tornado was also reported.
In Albacete, southwest of Valencia, 13 people were rescued from cars or from the roofs of buildings, emergency services told Europa Press. None was hurt.
Across the region, emergency services received hundreds of calls for help. Authorities mobilized the Military Emergencies Unit, a part of the Spanish armed forces that provides disaster relief.
In Murcia, authorities warned people not to go out in their cars.
The local Spanish government representative in Murcia, Francisco Jiménez, advised people to take "maximum precaution," adding that Thursday "is a good day to stay at home."
Local schools canceled classes Thursday and Friday for more than 300,000 students, according to Europa Press.
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