World Rugby chairman Bill Beaumont (left) gave a speech alongside Japan's Emperor Akihito during the opening ceremony
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Japan's Meteorological Agency (JMA) says Typhoon Hagibis is expected to reach the highest level of "violent".
The JMA added: "It could be the strongest to hit Japan this year."
World Rugby says it is heading in a "north-westerly direction" and could bring disruption to southern Japan.
The typhoon is predicted to hit the southern island of Kyushu on Saturday.
There are two fixtures on the island over the weekend - a potentially crucial match for Ireland against Samoa in Fukuoka on Saturday, while Wales face Uruguay in Kumamoto on Sunday.
World Rugby insists it has a "robust contingency plan in place" should the adverse weather impact tournament fixtures.
However, any games cancelled at the World Cup because of the weather are registered as scoreless draws.
Ireland need a bonus-point victory against Samoa to ensure their passage through to the quarter-finals.
Ireland's defence coach Andy Farrell said World Rugby is as "keen as we are to get this game played", adding: "The weather forecast changes all the time anyway, so we won't probably know until 48 hours out from the game.
"The boys haven't even spoken about it - we just go from day to day, get on with our preparations."
Wales might have already sealed their place in the quarter-finals before they face Uruguay with victory over Fiji on Wednesday, and head coach Warren Gatland says he does not want to "waste any negative energy on something that I can't change".
"We've had some updates in the past from World Rugby about potential weather stuff, and we will deal with that when it comes," Gatland told BBC Sport.
"We won't be thinking about that, we will just be focusing on the game."
'We're from Scotland - it doesn't matter'
Scotland face hosts Japan further north in Tokyo this weekend, a game they must win to stand any chance of reaching the last eight, and prop Gordon Reid says the weather "does not matter".
"We're from Scotland. Rain. Hail. It doesn't matter. We've coped with a lot more," said Reid.
"We're from Ayrshire and Glasgow and Edinburgh, well they're a bit posh in Edinburgh but rain, shine, snow, whatever, it doesn't matter."
Meanwhile, motorsport's governing body the FIA is also monitoring the situation ahead of the Japanese Grand Prix in Suzuka.
In 2014 the race was affected by bad weather, and was halted prematurely when Jules Bianchi crashed heavily, suffering severe head injuries which led to his death nine months later. BBC