Recent studies suggest that Omicron is less likely to make people seriously ill than previous Covid variants.
But the record number of people catching it has left health systems under severe pressure, said WHO chief Dr Tedros Adhanom Ghebreyesus.
On Monday, the US recorded more than one million Covid cases in 24 hours.
The WHO - the UN's health agency - said the number of global cases has increased by 71% in the last week, and in the Americas by 100%. It said that among severe cases worldwide, 90% were unvaccinated.
"While Omicron does appear to be less severe compared to Delta, especially in those vaccinated, it does not mean it should be categorised as mild," Dr Tedros told a press conference on Thursday.
"Just like previous variants, Omicron is hospitalising people and it is killing people.
"In fact, the tsunami of cases is so huge and quick, that it is overwhelming health systems around the world."
Omicron is highly contagious and can infect people even if they are fully vaccinated. However, vaccines are still pivotal as they help protect against severe disease that could put you in hospital.