WHO spokeswoman Dr Margaret Harris said France, Spain, the UK, the Netherlands and Russia accounted for the majority of cases which increased by a third.
"The concern... is that intensive care units in hospitals are now beginning to fill with very ill people," she warned.
Russia reported a daily record of 320 deaths, pushing the tally to 26,589.
There has been a sharp increase in Italy too, with 221 fatalities announced in the past 24 hours. The total number of fatalities in Austria went above 1,000 on Tuesday.