But there are growing signs that the surge of infections caused by the Omicron variant, first identified in southern Africa and Hong Kong, is levelling off or even falling in some areas.
Britain's seven-day average of cases has fallen by 30,000 from its peak, Spain's prime minister has said infection numbers are stabilising and a French public health institute has said the wave will peak in mid-January.
"We see a number of places where the peak is being reached or has been reached. It may be a bit earlier than anticipated, but remember the region is very diverse," Hans Kluge, the World Health Organization's Europe director, said this week.
"So we have to keep in mind the eastern part of the region, the Central Asian republics, where this peak still may come."
Health officials in Sweden and Switzerland have said the peak in those two countries is projected to be reached towards the end of this month.
"We could get to the peak within the next two weeks if contacts among people stay on the same level. If people are more cautious, it will take longer," Tanja Stadler, head of Switzerland's COVID-19 science task force, told reporters on Tuesday.
The trend echoes the Omicron wave in Africa, which the WHO's Africa office said appeared to be plateauing, making it the shortest surge in cases to date.
Denmark, where cases are dominated by Omicron, eased some restrictions this week, with the health minister saying the epidemic in the country was now under control.
Britain's Office of National Statistics has said the growth in infections has slowed in England. One in 15 people were estimated to have been infected in the week ending Jan. 6, the same as the previous week.
Despite the positive signs, politicians remain cautious.
British Health Secretary Sajid Javid said on Thursday that while the rate of hospitalisation was starting to slow, the health service would remain under pressure in the next few weeks.
"Omicron’s far greater transmissibility still has the potential to lead to significant numbers of people in hospital," he said.
He said there were encouraging signs that infections were falling in London and the east of England but "we're still currently seeing infections rise in other parts of the country and the data does not as of yet reflect the impact of people returning to work and school" after Christmas and New Year.
Scotland, which introduced tougher restrictions to combat Omicron than England, will start lifting those measures on Monday.
But, showing the stabilisation in case numbers is not being seen everywhere, Italy's National Health Institute said on Friday that weekly incidence and hospital bed occupancy continued to increase this week.
German virologist Christian Drosten warned on Friday that there were far too many Omicron cases and that this reduced any gains from it being milder than other variants, and Germany's health minister said more coronavirus restrictions might be needed if hospitals are overwhelmed. With Omicron initially spreading quickly among younger people, epidemiologists have said its impact on hospital admissions might be unpredictable as it moves into older age groups, even if headline case numbers come down.
But the ZOE COVID Symptom Study app, which collects data on self-reported symptoms to estimate prevalence in Britain, has found the Omicron wave has peaked, and that cases among the elderly have steadied at a low level.
"Just as it went up very fast, it also came down very fast and I think it is good news, it means that there will be easing of pressures on the hospitals," Tim Spector, lead scientist on the app, told Reuters.
Even so, the Omicron variant will not disappear, he said.
"It's just so infectious, there's no way we can pretend that it's going to get down to trivial levels, but it should be it should be manageable levels," he said.
Alistair Smout and Nikolaj Skydsgaard
(Reporting by Alistair Smout in London, Nikolaj Skydsgaard in Copenhagen, Emma Farge in Geneva, Clara-Laeila Laudette in Madrid, Emilio Parodi in Milan, Maggie Fick in Nairobi, Miranda Murray and Kirsti Knolle in Berlin, Editing by Timothy Heritage) ((email@example.com; +44 207 542 7064; Reuters Messaging: firstname.lastname@example.org))