Many of those calling are asking for advice about school or university and how to manage travel plans, Slater said.
It remains very important for people to register if they are going into self-isolation.
The disease - now officially named Covid-2019 - has infected more than 44,000 people worldwide and killed 1113, according to official reports.
The vast majority of deaths have been in mainland China, with 1068 of them in Hubei province, where the outbreak began.
Bloomfield said he would be very surprised if people arriving from China were not aware of the self-registration process.
Bloomfield said he would be very surprised if people arriving from China were not aware of the self-registration process.
He said under the Health Act there were powers to require people to self-isolate. If people were refusing to self-isolate the ministry would be following up with those people to see if "further action" needed to be taken.
But he believed people understood the importance of self-isolation - although it was "no small ask" to quarantine themselves for 14 days.
Healthline is contacting people every day if they are distressed or have welfare needs, while other people are being contacted every few days.
Bloomfield said cruise ships and other maritime traffic had been part of the planning for coronavirus since the start,
Before the coronavirus outbreak, cruise ships were already required to notify authorities in port if anyone onboard was unwell, Bloomfield said. He was confident that process would continue,
Slater said there had been "some" phone calls from people reporting on others who they thought should be in self-isolation. In the majority of cases that had been due to misunderstanding of the conditions surrounding self-isolation or the dates when it was imposed.
Bloomfield said the latest information regarding the disease-stricken Diamond Princess was that there were still only 2 New Zealanders infected with coronavirus onboard - the others were however in isolation like all passengers.