In a statement released at midnight on Friday, organizers also reiterated that the Games would go ahead as scheduled.
"The organising committee continues to work closely with all related organizations to prepare for a safe and secure Tokyo 2020 Games. There are no considerations of canceling the Games, nor will the postponements of these activities have an impact on the overall Games preparation."
The training was scheduled to take place on Saturday for those who had applied for field cast positions.
"In accordance with the government's policy for preventing the spread of infectious diseases, we will also evaluate the immediate need for each Games-related event on a case-by-case basis.
"At all Tokyo 2020 events, we ask that all participants take appropriate measures to ensure that all will be able to participate in safety and with peace of mind," the statement added.
More than 700 people have tested positive for the virus in Japan - the highest total of any country apart from China - although the majority of cases, around 634, have been found on the Diamond Princess cruise ship quarantined at Yokohama Port.
A number of sporting events have been affected, with medical experts in Japan advising against staging large events.
Both the Tokyo Marathon and the Nagoya Women's Marathon have canceled entries for the general public. A test event for the Paralympic event boccia, due to take place on February 28, was postponed by the Japan Para Sports Association.XINHUA
