The International Olympic Committee has insisted the Tokyo 2020 Games will go ahead as the Olympic torch was lit in ancient Olympia.
Thursday's ceremony in Greece was the first since 1984 to be held without spectators because of the ongoing concern over coronavirus.
IOC president Thomas Bach said organisers had "outstanding support and co-operation on all levels of government".
The Games are due to start on 24 July.
Bach told the small crowd of invited guests the IOC was happy with the measures being taken to avoid cancelling or postponing this summer's event in response to the global outbreak.
"Nineteen weeks before the opening ceremony of the Games we are strengthened in our commitment by many organisations around the world taking significant measures to contain the spread of the coronavirus," the IOC president said.
"When the flame returns to Tokyo after 56 years, hope will light the way across the entire country."
Greece's Anna Korakaki, a shooting gold medallist at Rio 2016, made history by becoming the first female torchbearer to start the Olympic torch relay.
Coronavirus - a fast-moving infection originating in China - has spread to more than 110 countries and claimed more than 4,200 lives.
The World Health Organization this week officially described it as a pandemic.
Tokyo Games chief Yoshiro Mori says any talk of a postponement is "outrageous", while on Thursday Tokyo governor Yuriko Koike said she believed cancellation was not an option, although she acknowledged that the pandemic designation would affect future discussions.