Yuriko Koike, Tokyo’s governor, said in an emergency news conference on Wednesday evening that people should avoid unnecessary outings until April 12.
Ms Koike said: “To avoid an overshoot in infections, the cooperation of Tokyo residents is critical. I ask you to act with a sense of crisis.”
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The Japanese capital has become the most-affected part of the country, with 41 cases reported on Wednesday and another 45 announced on Thursday.
More than 250 people have now tested positive for the virus in the city.
Although Japan has not implemented strict restrictions on movements like in other countries, its government is preparing a taskforce to deal with the crisis.
However, Yasutoshi Nishimura, the economy minister, said that the government was not yet thinking of declaring a state of emergency.
Japan has confirmed 1,314 cases and 45 deaths from the illness. These figures exclude the 712 infections and 10 deaths from the Diamond Princess cruise ship, which was anchored near Tokyo last month.
As a result of the outbreak, the country’s government and the International Olympic Committee have agreed to postpone the Tokyo Olympics by a year to 2021.
Elsewhere, health care experts worry about the spike in the number of coronavirus cases in Hong Kong.
Lam Ching-Choi, a member of Hong Kong’s executive council, told local broadcaster RTHK that the government is contemplating measures including a possible ban on gatherings at certain times.
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Mr Ching-Choi, who is also a doctor, said Hong Kong was now in a critical period.
Dr Ho Park-leung, head of the University of Hong Kong’s Centre For Infection, told local radio that the city’s public health system could collapse unless “lockdown-style” measures were introduced.
He warned that there would be “serious consequences” without these policies in place.
As of Thursday, Hong Kong had reported 410 coronavirus cases and four deaths.
Additional reporting from Reuters