The 308-foot (94-metre) boat, which ran aground, last week on a remote northern atoll, was not licensed to be in the country's waters.
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"What they were doing in Marshall Islands' waters is still unanswered," Chief Secretary Ben Graham said, adding that the government "is treating this as a crime scene".
The boat's 24-member crew arrived in the capital Majuro on Sunday after being rescued by a government patrol boat and a Chinese fishing vessel, with the US Coast Guard providing aerial reconnaissance.
The grounded vessel, the Ou Ya Leng No 6, is a frozen fish carrier and the owner is reported to be a squid supplier to longline vessels fishing in the region.
Sam Lanwi, deputy director of the Marshall Islands Marine Resources Authority, said the boat was "not licensed to operate in the Marshall Islands exclusive economic zone".
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Graham said investigators were interviewing the crew while other officials were heading to the scene of the incident to inspect the vessel and assess damage to the atoll.
"This is already an environmental disaster but there may be additional impacts if it begins leaking fuel," Graham said.
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