But glimmers of hope have begun to emerge from France, the Czech Republic and Belgium that tough restrictions might be starting to work.
Portugal, which like other European countries has seen cases and hospital admissions surge in recent weeks, has imposed a state of emergency.
It means some seven million people - around 70% of the population - have to stay home on weekday nights from 11pm to 5am for at least the next two weeks.
The restrictions are ramped up at the weekend, with people allowed out only in the mornings until 1pm, unless to buy essentials at supermarkets.
Hungary also imposed its strictest measures so far as Prime Minister Viktor Orban announced an 8pm to 5am curfew, except for commuters going to work.
All businesses in the country must close by 7pm.
Other measures in Hungary mirrored those becoming familiar across Europe as the virus surges, including limits on eateries, sports events and family gatherings, and remote learning for school and university students.
The restrictions kick in on Tuesday at midnight and will remain in place for at least 30 days.
"I know, we all know, that this will not be easy. The next weeks will be difficult. But the vaccine is within sight, we’ve got to hold out until then," Mr Orban said.
Last week, Hungarian Foreign Minister Peter Szijjarto announced that a small shipment of a Russian coronavirus vaccine would arrive in Hungary in December to undergo final tests, and that larger deliveries are expected in mid-to-late January.
The French government has gradually ratcheted up from localised curfews and closures of bars and other targeted businesses to what is now a full-blown nationwide lockdown, albeit with schools and essential businesses open.
Health Minister Olivier Veran said early indications are that the measures may be starting to slow the latest surge in France and that it would "have flared up faster and stronger" without them.
Belgian health authorities are confident that the hard-hit country’s partial lockdown has seen the peak of hospital admissions come and go.
Speaking at a news conference, virologist Yves Van Laethem said about 400 people were in hospital due to coronavirus complications on Sunday, compared with 879 a week earlier.
"Subject to an unpleasant surprise," the peak in hospital admissions was reached that day, Mr Van Laethem said.
Some 6,948 virus patients are being treated in Belgian hospitals now, down by about 500 patients from November 3.
To break the chain of transmission, Belgium has returned to partial lockdown measures including closing non-essential shops, bars and restaurants, as well extending the autumn school holiday.
In Germany, the health minister said increased infections seemed to be levelling off but that it was too early to talk of a trend.
Germany is one week into a four-week partial shutdown but new infections have continued to increase, reaching a new one-day record of 23,399 on Saturday.
Health minister Jens Spahn said on Monday: "We are seeing that the momentum is flattening, that we have less strong increases."
He added more progress is needed and that only later this week "at the earliest" will the restrictions’ effects become visible, "if at all".
"We don’t want less strong increases," he said. "We have to get the figures down."
Infections in the Czech Republic have started to decline after a two-month rise to record high levels and the number of people in hospital also dropped below the 8,000-mark.
Russia reported a record number of new daily infections on Monday with 21,798 cases, over 1,000 more than the previous daily tally.
The daily death toll of 256 was well below its highest count and officials say they are not considering imposing any national lockdown.