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The Financial Services Agency ordered Coincheck to raise its standards after the hack and gave the exchange until February 13 to submit a report on the heist, the safety of its systems, and measures it would take to prevent a repeat.
Coincheck said on Friday it would allow customers to restart yen withdrawals on Tuesday.
The exchange, which froze all withdrawals of yen and digital currencies following the theft, said it had confirmed the integrity of its system security.
Coincheck has received withdrawal requests from customers totalling about 30 billion yen ($280 million), a person with direct knowledge of the matter told Reuters last week.
Still, the exchange said it would keep restrictions on cryptocurrency withdrawals until it could guarantee the secure resumption of its operations. It did not give further details.
The Coincheck heist exposed flaws in Japan's system of regulating cryptocurrency trading, and raised questions over the country's dash to oversee the industry - a move that was in sharp contrast to clampdowns by policymakers in countries such as South Korea, China and India.