A joint statement by the Public Health Ministry and Port Authority said the captain of the Braemar reported four Filipinos, two British citizens and two U.S. citizens were under medical observation for symptoms such as fever, coughing, or breathing difficulty.
Fred. Olsen Cruise Lines said in an emailed statement that it had reported "a small number of influenza-like cases on board. Our medical team has now advised that they are all feeling better. No guests or crew are, or have been, displaying symptoms that are considered to be consistent with those of Coronavirus."
Officials said the ship was carrying 1,128 passengers and 384 crew members. The cruise line said it was "awaiting advice on the next steps" and "liaising with a number of airlines to secure onward travel for guests."
"It is our opinion that this is an overreaction by the Dominican Republic,'' Fred. Olsen said in a written statement.
The cruise line's website shows the ship had been due to pick up another load of passengers and set off on a new cruise Thursday night.
Public Health Minister Rafael Sánchez Cárdenas said the ship already had been barred by another port, which he did not specify.
Meanwhile, passengers on another vessel at the Mexican island of Cozumel faced yet another day in which they weren't allowed to get off the ship, after they had been previously turned away from two ports.
The MSC Meraviglia, turned away by two nations due to fears of the virus outbreak, docked at Cozumel on Thursday and President Andrés Manuel López Obrador said passengers would be allowed to disembark.
López Obrador said Mexico had to act with "humanity"after the ship was refused entry at ports in Grand Cayman and Jamaica.
But Alejandra Aguirre, the health secretary of the coastal state of Quintana Roo, said two people had been detected with acute respiratory infections not believed to be the new coronavirus and that other passengers wouldn't be allowed off until tests on those two came back later Thursday.
The two were identified as a 27-year-old male crew member from the Philippines and a 30-year-old female passenger from France.
MSC said in a statement that the two passengers were now symptom-free and the ship would remain in Cozumel. Assuming clearance to disembark is given, passengers would be free to tour Cozumel through the end of Friday.
The cruise line had expressed frustration with the rejections, which came after it reported the crew member was sick with common seasonal flu.
"The ship is being allowed to dock and the passengers, those who are aboard the cruise ship, can disembark," López Obrador said, adding that health inspections will be carried out.
"We cannot act with discrimination," he said. "Imagine if a ship arrived and it wasn't even allowed to dock, and they were told, 'Keep going on your way, see where you can dock.' That is inhuman."
He added "we cannot close our ports, nor can we close our airports."
"Imagine the desperation and everything it implies, almost 5,000 people on a ship and they cannot get off," he said. "Why such backward attitudes?"
The case of the Meraviglia illustrated the crisis of nerves over the COVID-19 virus. Mexico has no confirmed cases and MSC Cruises said the crew member had only common seasonal flu, had been placed in isolation and had "nearly recovered."
Local media showed a small knot of Cozumel residents near the cruise ship dock demanding that passengers not be allowed to disembark, citing fears about potential contagion or effects on the tourism-dependent economy.
Just minutes after López Obrador spoke Thursday, the governor of the Quintana Roo state, where Cozumel is located, confirmed the ship had docked, but said "no authorization has been given" yet for passengers to disembark.
Gov. Carlos Joaquin wrote that health inspections would have to be carried out first.