"We have said we were afraid that the cost could reach three trillion yen," Koike said.
"What it actually costs at the end of the day is very important."
Last month Koike and Bach agreed to discussions by the IOC, Tokyo 2020 organisers, the Tokyo metropolitan government and the Japanese central government to explore ways to achieve savings.
Koike said that the venue for canoeing and rowing will be kept in Tokyo as planned but vowed to build it at a sharply reduced cost.
She had proposed moving the event 400 kilometres (250 miles) north of Tokyo to Miyagi prefecture, one of the areas hardest hit by Japan's 2011 tsunami disaster.
But the idea faced resistance from Tokyo 2020 organisers who argued that changing venue plans was impractical and could actually end up costing more.
Koike also said that Tokyo will build a new aquatic centre with 15,000 seats, smaller and cheaper than the original plan for a 20,000-seat facility.
"Tokyo views costs seriously," she said at a meeting of the four parties where she made the announcement.
But she said about another month will be needed to decide whether to build a new volleyball venue in Tokyo or use an existing one in Yokohama, south of the capital.
Muto promoted the construction of a new volleyball venue in Tokyo, which could continue to be used as a sports arena.
"The Yokohama arena is a fantastic facility," he said at the meeting. "But issues have been raised by the IOC's technical team about its surroundings."
Problems of access for athletes, security and management of spectator traffic were among concerns voiced by Olympic experts about the facility, he noted.
IOC vice president John Coates, who also participated in the meeting, expressed satisfaction with the discussions, but said that overall costs must come down significantly.
"The IOC is confident that further savings can be achieved," Coates said, adding the he felt the organising committee's current budget cap is still too high.
"IOC has not agreed to that amount of money," he told reporters of the commitment to cap costs at 2 million yen.
"We think that the operational cost of the Games can be delivered significantly less than that."
Last month, IOC President Thomas Bach said that while the Olympic authority was concerned about rising costs for the Tokyo Games, the experience of the athletes had to remain a priority for any planning.
In a video message to a debriefing in the Japanese capital on the Rio Olympics, IOC chief Thomas Bach hailed them as "marvellous games" held in a "marvellous city."
"Organising the Olympic Games is an intensive process that requires creativity, discipline and collaboration with many people and stakeholders," he said.
"Most importantly, it requires unwavering commitment."
