Record virus cases in Tokyo as more regions weigh emergency
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Japan's vaccination programme started slowly, and only just over 25 percent of the population has had two jabs.
"I want young people to get vaccinated. Young people's behaviour is the key. I'm asking them please for their cooperation," Koike said.
Japan has seen a comparatively small coronavirus outbreak, with around 15,000 deaths despite avoiding harsh lockdowns.
The state of emergency in place in Tokyo mostly limits bar and restaurant opening hours and bans them from selling alcohol, though experts have warned compliance is dropping and cases are surging among young people.
The spike in cases is likely to increase scrutiny of the Olympic Games, with persistent concerns over whether the event could drive infections.
Olympic participants face various restrictions, including regular testing and limits on their movement.
And 124,358 tests of Olympic athletes and team officials this month revealed just 22 confirmed positive cases, according to Tokyo 2020 organisers. The figure does not include tests at airports.
Government spokesman Katsunobu Kato called on Japanese to avoid meeting and drinking in groups, suggesting people "watch the Olympic Games at home."
Fans are barred from almost all Olympic venues, though people have been showing up at competitions on public roads.
But Tokyo resident Takahiko Nimomoya said he was worried about the rising cases.
"I think the government isn't feeling the seriousness of the situation," the 55-year-old told AFP.
"They are just focusing on the Olympics."