"They are asked if they have any symptoms of illness and questions about contact with anyone suffering from Ebola virus disease, such as living in the same household or providing medical care," he said.
"If there is any concern, they will be given a further health assessment."
Screening was introduced at the country's border on August 10 and of the 58 people screened, 31 were New Zealand passportholders.
Hunt said it wasn't possible to quantify the risk of Ebola, and the risk to New Zealand remained very low, but health workers were still familiar with managing infectious diseases.
"In the unlikely event that someone with Ebola arrived in New Zealand, local and international expert advice is that it would be well contained in countries with health services like ours," he said.
He added that a technical advisory group had been set up so the Ministry of Health could check that the precautions being taken here were appropriate.
If a person in New Zealand was or was thought to be infected, he or she would likel be treated at one of the country's major hospitals.
Coleman said that Ebola was not easy to catch. "It is not spread through the air, and infection requires contact with infected bodily fluids. Existing isolation facilities and infection control protocols in our hospitals are suitable for treating a suspected or confirmed case of Ebola."
The death toll from the Ebola outbreak in West Africa has topped 4000. The Ministry of Foreign Affairs and Trade confirmed 47 New Zealanders were currently in West Africa.
Confirmed and suspected cases of Ebola have been reported in Guinea, Liberia and Sierra Leone. Only a small number of commercial airlines continue to operate out of those countries and most land borders are closed.
A travel warning by Mfat said New Zealanders in West Africa should consider how current, and potentially, more extensive travel restrictions could impact on plans to vacate Ebola-affected countries.
It was imperative that those in neighbouring Nigeria and Senegal monitored the situation "extremely closely".
Those who were in West Africa were warned to avoid direct contact with blood and other bodily fluids of people with Ebola or unknown illnesses, maintain strict standards of hygiene, avoid close contact with or handling of wild animals and avoid handling raw or undercooked wild meat.