Abe added the International Olympic Committee (IOC) would have the final decision whether Tokyo 2020 goes ahead.
"We will overcome the spread of the infection and host the Olympics without problem, as planned," Abe said.
Japan has had more than 1,400 cases and 28 deaths resulting from coronavirus.
The Tokyo Games is expected to cost about 1.35 trillion yen (£10.26bn), organisers said in December.
