The company said 158 crew members had been tested, with 120 tests coming back negative for COVID-19.
The ship is currently moored in Tromsø, Norway, with no guests on board.
Four crew members were confirmed positive on Friday.
None of the 154 crew members still aboard the ship – including the 29 new positive tests confirmed on Saturday – showed signs of illness or symptoms of COVID-19.
“We are now focusing all available efforts on taking care of our guests and colleagues. We are working closely with Norwegian national and local health authorities for follow-up, information, further testing and infection tracking, ”said Rune Thomas Ege, vice president of global communications.
The first four infected crew members were isolated several days ago due to other symptoms of the disease, showing no symptoms of COVID-19. They were tested regularly before being admitted to hospital in Tromsø, Norway on Friday morning.
Hurtigruten is in contact with all passengers who were on board the July 17 and 24 departures of the Roald Amundsen.
209 passengers on the first trip and 178 passengers on the July 24 departure will be quarantined in accordance with Norwegian health authority regulations, according to a statement, with the company saying it will also help customers with transportation, accommodation, food and other needs.
The Roald Amundsen was due to sail to Svalbard on Friday afternoon. This trip is now canceled. The next cruise with the ship is not scheduled until September.