Navy officials also said that several sailors started experiencing symptoms of COVID-19 after returning to the ship.
The Roosevelt has been preparing to return to sea in recent weeks, but Navy officials have not issued an update on the number of cases on board since the end of April, when 1,102 sailors of the ship's 4,800-strong crew were reported to have an active case of the virus.
The Navy installed a screening process for recovered sailors to return to the ship after two negative tests. The Roosevelt, meanwhile, underwent intensive cleaning and sailors quarantined or received treatment on the island.
The new positive cases may not prevent the vessel from returning to sea, but instead the ship may embark with a reduced crew, officials said.
The coronavirus outbreak on the aircraft carrier touched off a political firestorm this spring, as its captain, Brett Crozier, was dismissed after a memo on the subject went public. The acting secretary of the Navy, Thomas Modly, who fired Crozier and subsequently called him "stupid," later resigned.