The city has been arguing with the central government over how costs of the new stadium will be shared.
The government said on Monday it expects overall costs will soar to $2 billion, way up from the original estimate of $1.3 billion.
Coates said the stadium is the responsibility of the central government, and isn't bound by the cost-cutting guidelines of the International Olympic Committee's Agenda 2020 reforms.
"(The National Stadium) was always a project that was outside the budget of the organizing committee and its principal backer, the Tokyo municipal government," Coates said. "It's not a matter that has to be subject to the principles of Agenda 2020."
Coates stressed that the stadium's use will go well beyond the 2019 Rugby World Cup then the Olympics.
Tokyo has revised its Olympic venue plan to incorporate more existing venues, and Coates said these changes have resulted in a saving of $1.7 billion.
Cycling's venue remains a contentious issue. Tokyo organizers have proposed moving the venue to the Izu Peninsula, more than two hours from Tokyo. That has made the International Cycling Union unhappy.
"We are still involved in discussions with the UCI," Coates said. "It's well known that we are exploring using Izu, an existing venue that can be increased in capacity. ... What led us to look to go out there was the fact that original planning was for a temporary velodrome at a cost of $180 million that would be lost afterward."
During his two-day visit as part of the IOC evaluation commission, Coates toured the taekwondo, wrestling, and fencing venues which have been moved from central Tokyo to neighbouring Chiba prefecture east of the capital. The Makuhari Messe complex in Chiba is about a 30-minute train ride from downtown Tokyo.
"We're very pleased with the progress that's been made so far," Coates said.Suggest a correction