Health leaders said infections and deaths globally from Covid-19 are expected to increase "considerably" when global figures are published later on Tuesday.
It comes as the WHO counted more than 334,000 total cases globally on Monday, prompting warnings the world was entering a critical period in the outbreak.
The latest warnings come as stay-at-home restrictions were increasingly strengthened in European and North American countries, including the UK.
Dr Harris said: "The outbreak is accelerating very rapidly and the case numbers we received overnight will put that up considerably".
The US, which has more than 46,000 coronavirus cases and 530 deaths, could soon overtake Italy in the number of people to have tested positive.
Authorities say the US is on track to eventually overtake China's nearly 82,000 infections - adding how soon that happens, depends on how seriously Americans take the state-at-home restrictions.
For most people, the new coronavirus causes only mild or moderate symptoms.
Speaking on Monday, WHO chief Dr Tedros Adhanom Ghebreyesus urged countries a cross the world to "attack" the virus by "testing every suspected Cobid-19 case, isolating and caring for every confirmed case, and tracing and quarantining every close contact".
He continued that "we are not helpless bystanders", but noted that it took 67 days to reach 100,000 cases worldwide but just four days to go from 200,000 to 300,000.
He added: "We can change the trajectory of this pandemic."
People cleared by health authorities will soon be able to leave the province after midnight, though Wuhan itself will remain locked down until 8 April.
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Meanwhile in New York, now one of the world's biggest virus hotspots, authorities have rushed to set up the thousands of hospital beds needed to protect the city's 8.4 million people.
More than 12,000 people in the city have tested positive for coronavirus and 125 have died - a state-wide lockdown took effect on Monday.
New York governor Andrew Cuomo has warned: "This is going to get much worse before it gets better".
In Italy, Spain and France, the pandemic is pushing national health systems to their breaking points.
The number of virus-related deaths in Italy now stands at more than 6,000, the highest death toll of any country.
Officials said Monday the virus had claimed just over 600 more lives, down from 793 two days earlier, offering some glimmer of hope.
Spain announced 6,584 new coronavirus infections on Tuesday, taking the overall total to 39, 673.
The number of deaths also jumped by a record number of 514 to 2,696.
The risk to doctors and other medical staff on the frontlines, however, remains high - Italy has seen at least 18 doctors die after testing positive for coronavirus, while in Spain, some some 5,400 health workers have been infected.
An ice rink in Madrid is now being used as a makeshift morgue to cope with the rising number of deaths from the virus.
In contrast to other European nations, German health authorities offered some hope.
Officials said the country has flattened the exponential spread of the virus - which has already infected nearly 30,000.
Chancellor Angela Merkel's government approved a massive new aid package to cushion the economic fallout of the outbreak.