But King denied an application filed by lawyers for the migrants that sought to ban the public from all hearings.
The men were detained by police on Friday, after the military seized a mysterious freighter called the "Ocean Lady" off Canada's west coast.
Officials have said they suspect human smuggling in the case, and Canada's government has warned it will crack down on migrants who jump formal refugee and immigration queues to make refugee claims.
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"We need to do a much better job of shutting the back door of immigration for those who seek to abuse that asylum system," Immigration Minister Jason Kenney told The Globe and Mail newspaper.
Detention hearings for the remaining 74 men will be heard throughout the week as soon as logistically possible,