National are calling for the Government to significantly step up its efforts to prevent the deadly coronavirus taking hold in New Zealand, including giving more power to customs officials to probe travellers' health.

But the party's health spokesman, Michael Woodhouse, has stopped short of calling for New Zealand to reject all inbound flights from China, something Act Leader David Seymour has said should be considered.

At last count, almost 60 people have died in China, with thousands more confirmed to be infected.

Cases have been reported in the US, Europe and Australia.

Health Minister David Clark said this morning there have been no confirmed cases of coronavirus in New Zealand.

But, in a statement, the Lakes District Health Board revealed three members of a 19 person tour group were assessed at Rotorua Hospital yesterday as they might have been exposed to someone with the disease in a flight to Sydney last Monday.

They were found to have no symptoms, but a spokesperson said a range of tests were conducted regardless.

This morning, officials' screened 564 passengers arriving at Auckland Airport from China.

A spokesman confirmed that no passengers were displaying symptoms of the deadly virus.

But Woodhouse, who has been critical of the Government's response to the outbreak so far, said more needed to be done to make sure the disease does not take hold.

For example, he said customs officials should be required to ask arriving passengers if they feel unwell at airports.

He also wants to see public health staff in the arrivals halls of all international airports actively screening passengers.

Currently, health officials are on-site at just two airports, Auckland and Christchurch, and screening is not mandatory.

Woodhouse said it should be.

He said it's not at a point yet where the Government needs to be rejecting planes from China.

But he has called on the Government to beef up its plans, in case the outbreak does reach New Zealand's shores.

"This includes ensuring general practitioners and public hospitals are familiar with protocols for managing international travellers presenting coronavirus symptoms."

He also wants to ensure that sufficient protective equipment is available to health providers in the event of an outbreak.

"This should be the bare minimum in an event such as this."

But Seymour said the Government should be considering the possibility of turning away all flights into New Zealand from China.

"David Clark says he is simply following the advice of the World Health Organisation. But it isn't the World Health Organisation's job to calculate the risks and benefits of continuing to accept travellers from China."

He said that was the job of New Zealand's Government.

"Clark must explain his rationale for continuing to allow flights to arrive."