It will be the first time the Japanese capital has hosted the Games since 1964.
The decision to launch the new fund is widely seen as a softening of the elite sport body's "no compromise" approach, under which only sports with an expectation of winning a medal at Olympic or Paralympic Games receive support.
The Tokyo Organising Committee said Friday that the goal of collecting over 30kg of gold has been nearly completed, with the necessary amount of precious metals expected to be gathered by the end of March.
The scheme planned to collect 30.3 kilograms of gold, 4,100kg of silver and 2,700kg of bronze in order to produce the medals, and on Friday it was confirmed that those targets were expected to be achieved by the end of March.
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Collection of the metals from discarded small devices began in April 2017. While the target for bronze and silver has been attained, the gold remains bit short.
"It is estimated that the remaining amounts of metal required to manufacture all Olympic and Paralympic medals can be extracted from the devices already donated", Tokyo 2020 organisers said.
By November a year ago, 47,488 tonnes of discarded devices had been collected, with the public handing in another five million used phones to a local network provider.
The designs for the Tokyo 2020 medals will be unveiled later this year. The IOC requires gold medals to contain at least six grams of gold and 92.5 percent silver, and gold medals at the 2018 PyeongChang Olympics were worth about $570 each.