And the pandemic has shown that "nobody is safe until everyone is safe".
The signatories, who include the head of the World Health Organization, Dr Tedros Adhanom Ghebreyesus, say: "At that time, following the devastation of two world wars, political leaders came together to forge the multilateral system.
"The aims were clear: To bring countries together, to dispel the temptations of isolationism and nationalism, and to address the challenges that could only be achieved together in the spirit of solidarity and co-operation - namely peace, prosperity, health and security."
The leaders say that in the same spirit, countries must now "be better prepared to predict, prevent, detect, assess and effectively respond to pandemics in a highly co-ordinated fashion".
A new treaty would help to establish better systems for alerting people about potential pandemics, they say, while also improving the sharing of data and distribution of vaccines and personal protective equipment.
"There will be other pandemics and other major health emergencies. No single government or multilateral agency can address this threat alone. The question is not if, but when.
"The Covid-19 pandemic has been a stark and painful reminder that nobody is safe until everyone is safe."
The letter continues that at a time when Covid-19 has exploited our weaknesses and divisions, world nations must seize this opportunity and come together as a global community for peaceful co-operation that extends beyond this crisis./bbc