The fire is out at the platform in Grand Isle Block 115 and an investigation into the cause is underway, the agency said in a statement.
The platform was shut two weeks ago and was not producing at the time of the blaze, the Coast Guard said.
The two workers who were rescued were the only people aboard the platform at the time of the fire, Petty Officer Steve Lehmann said.
The investigation is being conducted by the U.S. Bureau of Ocean Energy Management, Regulation and Enforcement, Lehmann said.
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