Asked at a news conference if the global sporting showpiece might still be cancelled, Toshiro Muto said he would keep an eye on infection numbers and liaise with other organisers if necessary.
"We will continue discussions if there is a spike in cases," Muto said.
"We have agreed that based on the coronavirus situation, we will convene five-party talks again. At this point, the coronavirus cases may rise or fall, so we will think about what we should do when the situation arises."
A spokesman for Tokyo 2020 later said organisers were "concentrating 100 percent on delivering successful Games".
Rising Covid-19 cases in Tokyo have cast a large shadow over an event that, having already been postponed last year because of the pandemic, will now take place without spectators. Japan this month decided that participants would compete in empty venues to minimise health risks.
There have been 67 cases of Covid-19 infections in Japan among those accredited for the Games since 1 July, when many athletes and officials started arriving, organisers said on Tuesday.
Japan, whose vaccination programme has lagged that of most other developed nations, has recorded more than 840,000 cases and 15,055 deaths and Games host city Tokyo is experiencing a fresh surge, with 1,387 cases recorded on Tuesday.
Muto, a former top financial bureaucrat with close ties to Japan's ruling party, is known for his careful choice of words, while officials are facing a domestic public angry about coronavirus restrictions and concerned over a possible spike in cases triggered by Games attendees arriving from abroad.
Organisers, for whom International Olympic Committee (IOC) President Thomas Bach said cancelling the event had never been an option, have promised to keep the Games "safe and secure".
But experts see gaps in an Olympic "bubble" that mandates frequent testing and has been designed to limit participants' movements.
Seiko Hashimoto, who sits alongside Muto as organising committee President, said that safety measures introduced to reassure the Japanese public had not necessarily done so, and that she was aware that popular support for the Games had dropped.
"I really want to apologise from my heart for the accumulation of frustrations and concerns that the public has been feeling towards the Olympics," Hashimoto told the same news conference.