Germany has also hit a two-month high on new infections, as nations grapple between staving off fresh outbreaks and reopening economies.
The European rises are echoed in far bigger increases across the rest of the globe, with record daily new-infection figures of around 280,000 in both of the past two days.
“While no country is unaffected, this rise is driven by high transmission in large and populous countries in the Americas and South Asia,” the World Health Organization (WHO) said in a statement on Saturday.
Barely a month after Spain ended its state of emergency, cities including Barcelona, Zaragoza and the capital Madrid have seen a surge in new infections, prompting the government to warn that a second wave could be imminent.
The Spanish health ministry reported more than 900 new cases of the virus on Friday. One football team in the second division, Fuenlabrada, now has 28 confirmed cases.
The BBC’s Guy Hedgecoe in Madrid says contagion among young people is a particular worry, as they have been gathering in large numbers in cities at night.