"Unless we do it all, (2 million deaths) ... is not only imaginable, but sadly very likely," Mike Ryan, head of the UN agency's emergencies programme, told reporters at the WHO's headquarters in Geneva on Friday.
His assessment came as the total number of deaths nine months since the virus was discovered in China neared the grim milestone of one million.
Many European nations, meanwhile, are struggling with new waves of infections as winter approaches.
Ryan said young people should not be blamed for the surge despite growing concerns that they are driving the spread after restrictions and lockdowns were eased around the world.
"I really hope we don't get into finger wagging: it's all because of the youth," he commented. "The last thing a young person needs is an old person pontificating and wagging the finger."
Rather, indoor gatherings of people of all ages were driving the epidemic, he said.
'Global responsibility'
The pandemic has spurred worldwide efforts to develop a vaccine to help defeat Covid-19, as well as efforts to try to ensure fair and widespread distribution.
"Whoever finds the vaccine must share it... This is a global responsibility and it's a moral responsibility," Australian Prime Minister Scott Morrison said Friday in a message to the virtual UN General Assembly.
"Some might see short-term advantage or even profit, but I assure you... humanity will have a very long memory and be a very, very severe judge."
Without a vaccine or effective treatment, social distancing and lockdowns remain among the few options for governments to curb the spread of the virus, making large gatherings like spectator sports and music concerts highly risky.
Casualties
The 2020 Tokyo Olympics, postponed for a year, were one of the biggest casualties, and Japan's new leader vowed to hold them in 2021 regardless of how the pandemic plays out.
But with continued spikes worldwide, there are concerns about whether the event will be possible even next year if the pandemic is not under control.
In a further illustration of the impact of the virus, authorities in Brazil -- which has the world's second-highest death toll -- indefinitely postponed Rio de Janeiro's carnival.
And just 1,000 fans a day are being allowed at the French Open, with organisers of one of the world's biggest tennis events saying it means "millions of euros up in smoke".
