A second crew member on the Diamantina cattle export ship berthed in Darwin has tested positive for COVID-19, with suspicions a third also has been infected.

The possible two new cases follow the confirmed infection of a 25-year-old crewman on Monday

Authorities said the second case involved a 35-year-old man while a 36-year-old man will require further testing.

Both have been transferred to Royal Darwin Hospital and placed in isolation.

The Diamantina arrived in Darwin from Indonesia on Sunday night.

The majority of other crew members have been transported to a separate section of the Howard Springs quarantine facility.

They will complete 14 days of mandatory supervised isolation unless the Diamantina’s operators elect to leave Darwin sooner, in which case they will be escorted back to the ship.

Some crew members are required to remain on board the Diamantina to comply with international maritime law. Testing will be undertaken and they are required to stay on board in self-isolation.

Those who came into contact with the ship will also be placed into isolation. However, they were wearing personal protective equipment when boarding the vessel and did not contact the infected men.

Northern Territory Health Minister Natasha Fyles said there was no indication anyone had breached the territory’s public health orders.

“We’ve certainly had very strong compliance to date and authorities have been appropriately engaged, whether it’s from Health, Maritime Safety or from police,” Ms Fyles told reporters on Tuesday.

“These vessels, not only do they bring goods that Australians need … these are vital supply chain vessels.”

The latest COVID-19 case takes the total number of coronavirus infections diagnosed in the NT to 76.

That number will rise by one if the 36-year-old is confirmed to have the disease.