"New Zealand takes its international obligation to come to the aid of ships in its waters that have put out distress calls seriously," he said.
"In that context, any crew movements are subject to health orders prioritising safety for New Zealanders."
The ministry in a response statement to the Herald said it this wasn't the first time ships with confirmed cases of the virus had come to New Zealand.
"... authorities and officials have experience in managing these situations ... all three of these ships currently docked in New Zealand are quarantined and all risk to the public has been minimised."
Crews from three vessels, a container ship and two fishing ships, are currently at the centre of multiple Covid-19 cases at the border. New Zealand has no community cases.
Crew members on the Mattina, in quarantine in Bluff, had now tested positive, the health ministry said on Tuesday.
The Marshall Islands-flagged vessel came into port on July 18 and all 21 crew members were tested after two crew members reported having symptoms. Following confirmation of the first two cases, further results confirmed another seven cases on the ship. The initial two symptomatic crew members joined the ship in Singapore on July 2 after providing negative pre-departure tests, said the ministry.
However, Herald inquiries show the ship called at Jakarta and Freemantle, Australia, before arriving in New Zealand waters.
Southern DHB was working with other agencies to decide the next steps for the Mattina, said the ministry. The crew remains on board the ship, which is quarantined in a secure area of South Port, inaccessible to the public, the ministry said.
Meanwhile, Spanish-flagged fishing ship the Playa Zahara is quarantined at Canterbury's Lyttelton Port after 13 of its 18 crew were transferred to a managed isolation and quarantine in Christchurch on July 18. Preliminary results of genome sequencing showed three crew had the Delta variant of the virus.
Swabs of the Playa Zahara crew were first taken on its arrival at Port Taranaki on July 13 after reports of a flu-like virus on board. The vessel was sent on to Lyttelton for appropriate support there. Five crew remain on board for vessel maintenance.
A second fishing vessel, the Viking Bay, is quarantined at Wellington's port after most of its crew were transferred to a quarantine facility last week. Twelve crew have the Delta variant of Covid-19.
The ministry said just over half the crew of the Viking Bay had been at sea since February.
Seafarer welfare is a huge concern in the sector due to the pandemic, with reports of crews being unable to set foot on dry land for up to and more than a year, according to reports.
Lyttelton Port chief executive Roger Gray told the Herald the port worked closely with Government authorities on arranging the safe arrival of the Playa Zahara and transfer of its crew to Christchurch MIQ facilities.
The safety of the port's staff and community was always top priority but the port also took the welfare of seafarers seriously, he said.
"... We believe every effort should be made to make sure they can safely access medical care."
"If we were not comfortable with procedures proposed regarding the berthing and arrival of the Playa Zahara we would have the right to say 'no' to having the vessel in Lyttelton.
"However, in this case, we were comfortable with the procedures in place. It is also worth noting that the berthing of Playa Zahara was conducted safely and effectively, as was the transfer of crew to MIQ facilities."
Port Taranaki chief executive Guy Roper said each and every vessel entering the port first had to have clearance from the Taranaki DHB.
The master of the Playa Zahara had responsibly advised there were symptomatic crew members aboard so "free pratique" or approval was not given, and the vessel came into the port under quarantine conditions on July 13 so Covid testing could be done, Roper said.
This involved the vessel being piloted remotely into and out of port, meaning no Port Taranaki pilot or other staff members went aboard. The vessel was moored at a special quarantine area and those tying it up wore full PPE and had no contact with crew.
The crew was tested by the health officials on the wharf beside the vessel, and the crew returned to the vessel before heading offshore to await the results. The wharf area was then washed down, Roper said.
