Games organisers have been working to slash costs after a study last year warned that expenses could balloon to four times the initial estimate made in the bid process.
The International Olympic Committee (IOC) is keen for Tokyo to set a good example by cutting costs in order to attract future candidate cities.
"We want to deliver fantastic Games but at the same time ... we don't want to use any public funds if we can help it," said Hidemasa Nakamura, the chief financial officer of Tokyo 2020.
"We will continue to try to reduce (costs) further."
The Tokyo Metropolitan Government accounts for $5.6 billion of the latest budget and Japan's central government $1.4 billion, according to the organisers' estimates.
"We are still looking at the overall Games with the big purpose of reducing costs overall, and in the process we need a clear explanation that is compelling, not just for Tokyo citizens but for all Japanese citizens," Tokyo Metropolitan Government official Tetsushi Koyama told a news conference.
Version one of the budget, issued in December last year, was projected at $14 billion. Version three is due out in December 2018.
IOC Vice-President John Coates said earlier this month he was confident significant savings would be achieved ahead of the Games but warned organisers needed to remain vigilant.
Tokyo 2020's Nakamura said he wanted to create a plan that would prompt Coates to say: "'You've done a good job'."
"I think there is a need to shrink costs further in version three and continue that in version four," Nakamura said.
(Reporting by Linda Sieg; Editing by Peter Rutherford)
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