Authorities had previously reported 20 dead, but have warned that the final figure is sure to be far higher.
Minnis has said that the storm caused "generational devastation."
The United Nations said 70,000 people in the Bahamas were in "immediate need" of aid.
Dorian, currently a Category 2 storm, was pounding the US states of North and South Carolina on Thursday night with strong winds and driving rain, bringing dangerous storm surge.
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