"This is a time for prudence, not panic. Science, not stigma. Facts, not fear," he said in a video message recorded on Friday afternoon.
Even though the situation has been classified as a pandemic, the UN chief said, it is one they can control.
"We can slow down transmissions, prevent infections and save lives. But that will take unprecedented personal, national and international action," he said.
Guterres said many are anxious, worried and confused. "That’s absolutely natural."
He said they are facing a health threat unlike any other in their lifetimes.
The UN chief said the virus is spreading, the danger is growing, and our health systems, economies and day-to-day lives are being severely tested.
"The most vulnerable are the most affected — particularly our elderly and those with pre-existing medical conditions, those without access to reliable healthcare, and those in poverty or living on the edge," he said.
Guterres said the social and economic fallout from the combination of the pandemic and slowing economies will affect most of them for some months.
"COVID-19 is our common enemy. We must declare war on this virus. That means countries have a responsibility to gear up, step up and scale up," he said.
"All of us have a responsibility, too – to follow medical advice and take simple, practical steps recommended by health authorities," he said.
The UN chief said the financial markets have been hard hit by the uncertainty and global supply chains have been disrupted. "Investment and consumer demand have plunged – with a real and rising risk of a global recession."
UN economists estimate that the virus could cost the global economy at least $1 trillion this year – and perhaps far more.
"No country can do it alone. More than ever, governments must cooperate to revitalise economies, expand public investment, boost trade, and ensure targeted support for the people and communities most affected by the disease or more vulnerable to the negative economic impacts," said the UN chief.
The UN said a pandemic drives home the essential interconnectedness of human family and preventing the further spread of COVID-19 is a shared responsibility for all.
The United Nations is fully mobilised, said the UN chief.
"We’re working 24/7 with governments, providing international guidance, helping the world take on this threat. We’re in this together – and we’ll get through this, together," said the UN chief.