The captain gave the order for the crew to enter the lifeboats at 4:30 EST and a rescue attempt by a US coastguard helicopter is under way.
The HMS Bounty Organization said it would assess whether the ship could be saved but its concern was for the crew.
HMS Bounty is a replica of the original Bounty, famous for its ill-fated trip to Tahiti and the West Indies in 1789.
Tracie Simonin, director of the HMS Bounty Organization, said that the ship began to experience difficulties at about 18:30 EST on Sunday when it lost power and was unable to continue “de-watering”.
“At that time we contacted the US coastguard for assistance,” she said.
“A C-130 plane was sent to their position, which was 90 miles south-east of Cape Hatteras, and then at 04:30 EST this morning the captain ordered all hands to abandon ship.
“All 17 crew were accounted for in the liferafts and a US coastguard helicopter is on the scene rescuing them now.”
Tracie Simonin added: “As far as we know the ship is still upright and we’re going to assess the situation to see if anything can be done to save the ship but at this point our main concern is with the crew.”
Tracie Simonin said everyone on board was American.
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