The warning came as it emerged the virus was present in Italy in December, months before its first confirmed cases and about the same time as the disease was first reported in China.
The virus, which has now killed more than 454,000 people and infected 8.4 million people worldwide, is surging in the Americas and parts of Asia even as Europe starts to ease restrictive measures.
Lockdowns imposed to halt the spread of the disease have caused crippling economic damage, but the WHO said the pandemic still posed a major threat.
“The world is in a new and dangerous phase. Many people are understandably fed up with being at home… but the virus is still spreading fast,” WHO chief Tedros Adhanom Ghebreyesus told a virtual press conference.
A vaccine remains months off at best despite several trials, while scientists are still discovering more about the virus, its symptoms and the extent to which it may have spread before being identified.
Italian researchers discovered genetic traces of SARS-CoV-2 — as the virus is officially known — in samples of waste water collected in Milan and Turin at the end of last year, and Bologna in January, the ISS institute said.
Italy’s first confirmed cases were not until February.
The results “help to understand the start of the circulation of the virus in Italy,” the ISS said.
Italy was the first European country to be hit by the virus and the first in the world to impose a nationwide lockdown, in early March.
In a sign of the persisting risks, ISS, Italy’s top health agency, also urged caution after last week seeing “warning signs” of virus transmission following two outbreaks in Rome.
“In certain parts of the country, the circulation of the virus is still significant,” ISS said in its weekly report.
Many European countries followed Italy into lockdown, and most have only begun reopening this month after painful shutdowns that devastated their economies.
Facing the biggest recession in the EU’s history, leaders on Friday held a virtual summit on the European Commission’s proposal for a 750 billion euro ($840 billion) rescue fund.
However they fell short of reaching a deal on a plan seen as a key gesture of the bloc’s solidarity and unity.
Opposition is fierce from the “frugal four” — Netherlands, Sweden, Denmark and Austria. But Italy and Spain that were the first and hardest hit by the pandemic were already crippled by overstretched finances.
‘Came from Europe’
Chinese scientists have said the virus likely emerged in a market that sold wildlife in the central city of Wuhan in December, but Beijing officials have recently suggested it may have originated elsewhere.
After largely bringing the virus under control and easing restrictions, China is now fighting a resurgence after finding a cluster centred on a market in Beijing.
Authorities launched a nationwide campaign to inspect food imports, while tens of thousands of people are also being tested and neighbourhoods have been locked down.
Chinese authorities said studies of genome data, which it had shared with the WHO, suggest the new outbreak in Beijing “came from Europe”, but is different from what is currently spreading there.
“It is older than the virus currently circulating in Europe,” Zhang Yong of the Chinese Center for Disease Control and Prevention (CDC) said.
He raised the possibility of the virus lurking in imported frozen food or in the wholesale market itself, resulting in similarities to older strains.
The United States still leads the world in the number of confirmed infections and deaths, with a recent surge in southern states, while the economy has also been hammered in a year when US President Donald Trump seeks re-election.
However top US expert Dr Anthony Fauci offered hope as he said in an interview with AFP that he did not see America returning to fresh lockdown.
He predicted it would instead focus on “trying to better control those areas of the country that seem to be having a surge of cases”.
Fauci said he was optimistic the world would soon have a vaccine to end the pandemic, calling early trial results “encouraging”.
Still, Apple said it was closing some stores in US states experiencing a surge in infections, reversing course after reopening many of its retail locations.
The Philadelphia Phillies baseball team also said five players and three staff tested positive for COVID-19 at the club’s Clearwater training base in Florida.
But normality is returning to cultural and sporting events disrupted by the virus.
Football returned to hard-hit South America on Thursday after a three-month hiatus with a Rio state tournament match in Brazil.
And in France, the nation of le grand amour, actors have started kissing again on film shoots.
“No, the kiss is not over with,” French Culture Minister Franck Riester declared when asked if social distancing was in danger of killing off love scenes altogether.
Actors must however be tested before they start smooching again.