Spain is taking new measures to cut a spike in coronavirus cases, amid fears of a more widespread "second wave".
Catalonia has closed its nightlife for two weeks but cities outside the north-eastern region are also seeing a surge.
The UK says all returning from Spain must self-isolate. Norway has similar rules and France has a travel warning.
France and Germany have also both seen new cases rise, 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.
There have been more than 15.7 million cases globally and more than 640,000 deaths, according to Johns Hopkins University.
What is happening in Spain?
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 government of Catalonia now says all nightclubs and late-night bars in the region are to close for the next two weeks. The Spanish defence ministry is also implementing an early response tracker system to prevent any upturn in cases in the military.
The 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.
Epidemiologist Dr Daniel Lopez-Acuna told the BBC the average age of cases could rise "because the transmission is going from the youngsters to the rest of the household, and certainly the elderly".
The UK says all those returning from Spain must self-isolate for 14 days from Sunday. This includes the Canary Islands and Balearic Islands, although those destinations are not included in the UK's new general warning to avoid all but essential travel to mainland Spain.
Norway has said it will also start quarantining people arriving from Spain, while France has warned its citizens not to travel to Catalonia.
Belgium has banned travel to Huesca and Lleida, with recommendations against travel to a number of other areas in Spain.
A Spanish foreign ministry spokeswoman said the country was safe, with only localised, isolated and controlled outbreaks.
Are other European nations concerned at spikes?
Most are seeing increases and outbreaks but want to keep economies functioning and hope any second wave will be regionally limited.
Belgium has slowed down its reopening amid a sharp rise in cases.
Italy is isolating arrivals from Romania and Bulgaria for two weeks after a number of imported cases.
French Prime Minister Jean Castex says people arriving from 16 countries where the virus is widely circulating will be subject to on-the-spot coronavirus tests.
France's health ministry said there were now more than 1,000 new cases each day in hospitals.
Germany said it might introduce compulsory testing for holidaymakers returning from high-risk destinations after infections hit a two-month high.
What are the global increases?
The trajectory is still worryingly upwards, says the WHO - more than a quarter of a million new cases for three days straight up to Friday.
One major concern is India, where there are now 1.3 million confirmed cases - 100,000 of them in just the past two days - with experts fearing the worst is still to come
One of those to have tested positive was the chief minister of the state of Madhya Pradesh, Shivraj Singh Chouhan, who urged people not to be careless.
The United States, Brazil and South Africa are also still showing sharp increases.
In other developments:
- Brazilian President Jair Bolsonaro announced on Saturday he was now negative for Covid-19 - more than two weeks after testing positive. He attributed his recovery to hydroxychloroquine, a drug still unproven in its effectiveness against coronavirus. And this year's New Year's Eve celebrations in Rio de Janeiro - which attract millions - are cancelled
- Vietnam is back on high alert after detecting its first locally transmitted case in about three months, a 57-year-old grandfather in the central city of Danang
- More than 10,000 health workers have contracted coronavirus in Africa since the start of the pandemic, the WHO says
- Hong Kong reported its highest ever daily total of new infections on Saturday - more than 130, with social-distancing measures extended
- Imported cases have pushed the number in South Korea to levels not seen since March
- The virus has also been surging in Japan, which recorded its highest number of new cases this week