Speculation about a delay from the July start date has grown since US President Donald Trump said organisers should consider a one-year postponement.
Abe and Trump held a call after those comments,prompting the US president to say on Twitter that the Olympic venue was magnificent.
But this may not be enough to assuage sponsors of the Games,who are increasingly nervous about the impact of the outbreak on the competition.
The Olympic Torch relay,in which the Olympic flame typically starts a tour around the host nation,is due to start in the Japanese prefecture of Fukushima in less than two weeks.
The tour of the torch through Greece has already been cut short.
"We will overcome the spread of the infection and host the Olympics without problem,as planned,"Abe told a news conference in Tokyo on Saturday,adding that delaying or cancelling the Olympics was"not a subject at all"in his call with Trump.