Just a few hundred officials and dignitaries were in the stands of the 68,000-seat venue to watch the spectacle which included Japan Emperor Naruhito declaring the Games open.
There is no indication so far the games will be cancelled. The International Olympic Committee has repeatedly said they are going ahead.
The statements by IOC's vice president come as questions continue to be raised about the viability of holding the Olympic Games this July, given the ongoing pandemic and an extension of a virus state of emergency in Tokyo and other parts of Japan.
IOC President Thomas Bach said he had the "full support" of the Japanese government to go ahead with the implementation of the Tokyo Games.
The letter sent by right groups to the International Olympic Committee says the IOC has “turned a blind eye to the widespread and systematic human rights violations being committed by the Chinese authorities.
The current rule 50 of the Olympics charter tries to uphold political neutrality for the Olympics but allows athletes to express opinions in interviews after their events.
Games chief Yoshiro Mori's comments come as medical experts express doubt over containing the pandemic sufficiently to hold an event drawing participants and spectators from around the world.
Last week, the IOC and Japanese organisers postponed the Olympics until 2021 amid the coronavirus pandemic.
The IOC has remained committed to staging the Tokyo Games as planned from July 24-August 9, saying on Tuesday after a meeting with international sports federations that measures against the virus were delivering results.
John Coates, who will have to go into government-mandated self-isolation when he returns to Australia this week from Olympic business in Europe, told the Sydney Morning Herald newspaper: “It’s all proceeding to start on the 24th of July.”
The IOC "is fully committed to a successful Olympic Games in Tokyo starting July 24", Thomas Bach told Japanese media in a conference call.
Athletes who break protest rules will face three rounds of disciplinary action.
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