"It's going to get tougher. In October, November, we are going to see more mortality", WHO Europe director Hans Kluge said.
It is only the second day since the beginning of Covid-19 pandemic that the total number of daily cases has exceeded 300,000, after 306,857 confirmed cases were reported on 6 September.
Restrictions banning social gatherings of more than six people have come into effect in England and Scotland.
Earlier, Tedros also urged the world not to delve into blame games regarding the COVID-19 pandemic, warning that such acts were detrimental to the fight against the pandemic.
"I think one would have to say that we are on the edge of losing control", Dr Mark Walport, the British government's former chief scientific adviser, told BBC radio.
"In recent years we have seen a recurring pattern. Fall and winter will be hard on everybody". On Friday alone, more than 51,000 new cases were reported in the 55 countries of the WHO Europe, which is more than the highest peak in April, according to the organisation.
Countries across Europe are recording a rising number of daily cases amid fears of a resurgence of the virus.
The biggest increases in infections were reported in India, the United States and Brazil.
The country also reported 14,768 new cases, taking the total caseload to 4,330,455.
"It's as if we wait for the plane to crash, then call for more safety inspections".
In a statement on Sunday, the World Health Organization said that there were 307,930 new cases globally in the last 24 hours, the highest single-day figure ever registered and about 1,000 more than the previous recording-setting daily caseload a week earlier, reports Xinhua news agency.