Life is "completely normal and safe" in Tokyo and the city's air and water are not affected by the leak from the tsunami-damaged facility, Japanese IOC member Tsunekazu Takeda said in the letter.
A copy of the letter, dated Aug. 27, was obtained Monday by The Associated Press. The International Olympic Committee is set to decide the 2020 host city in a vote on Saturday in Buenos Aires, Argentina.
Tokyo, long considered a favourite, is competing against Madrid and Istanbul.
A 300-ton leak of radioactive water was discovered at the Fukushima plant on Aug. 19, the fifth and worst leak since the plant had triple meltdowns after the massive earthquake and tsunami in 2011. Officials said most of the water is believed to have seeped underground but some might have escaped into the sea.
On Monday, Japan's top nuclear regulator raised concerns about hastily built storage tanks and their foundations at the plant after signs of new leaks of radioactive water.
Fukushima is 250 kilometres (155 miles) north of Tokyo and bid officials say the leak won't affect the city's plans to host the Olympics, but the timing of the incident is not helping its chances.
"You might have seen news reports about the situation at the Fukushima nuclear plant, in the northeast of Japan," Takeda said in the letter. "Please allow me to reconfirm that Tokyo remains completely unaffected.
"Life here, for all 35 million residents, is completely normal and safe and we do not foresee any change to that. The city's air and water are monitored daily and there remains no evidence at all of any issue, as confirmed by the Japanese government."
Tokyo has championed its bid as being the "safe pair of hands" at a time of global economic and political uncertainty. Japanese officials have also heralded the Olympic bid as a chance to lift the country's spirits following the earthquake and tsunami.
In a separate telephone interview with the AP, Takeda reiterated his position that the Fukushima leak wasn't a problem for the bid, saying Prime Minister Shinzo Abe and his government were tackling the problem.
"Food and water in Tokyo is absolutely safe," Takeda said. "It will not affect Tokyo's hosting of the games. The radiation levels are the same as in London and New York. Life is normal in Tokyo."
All three bid cities are saddled by serious issues.
Istanbul is seeking to overcome June's anti-government protests and police crackdown, a series of recent doping scandals and the escalating war in neighbouring Syria. Madrid has to deal with Spain's economic crisis and 27 per cent unemployment rate.
Saturday's vote will be held by secret ballot following presentations by each city. The prime ministers of all three countries will be travelling to Buenos Aires to lead the bid delegations.
Takeda welcomed Tokyo being seen as the front-runner. London bookmaker William Hill has the city as 4-7 favourite.
"I'm very happy everyone says so, but nobody knows until the final decision," Takeda said. "We will do our very best up until the final minute. I'm confident but only the gods know what will happen."
In his letter to IOC members, Takeda made a personal plea.
"Please entrust us with the games, and we will be proud but humble hosts and will return your games to you better than we received them," he wrote. "That is my commitment to you."