There are four more confirmed cases of coronavirus in Wellington and Dunedin.

Director-General of Health Dr Ashley Bloomfield confirmed three of the four new cases this afternoon and said they had recently returned from overseas.

Hours after the Ministry of Health update, a Dunedin high school student tested positive for Covid-19, and the student's school will close for at least 48 hours.

The latest cases takes the total number in New Zealand to 12.

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A Wellington man in his 30s and his father aged in his 70s had recently returned from the United States. Neither require hospital care. They arrived in Auckland on American Airlines flight AA83 from Los Angeles on Saturday March 14.

The younger man was unwell on the flight, the father became unwell about a day later.

The pair then flew from Auckland to Wellington on Air New Zealand flight NZ419 in seats 1B and 1C.

The two men had been picked up from Wellington airport, then spent the weekend at home. They called ahead before going to the doctor, which was the correct thing to do, Bloomfield said.

The Dunedin case also recently returned from overseas.

This is a man in his 40s who came from Germany.

Focus: Passengers arriving at Auckland International Airport say their plans have been thrown into disarray after new travel restrictions.

He only developed symptoms five days after returning, so there was no risk to others on the plane, Bloomfield said.

Two of the man's relatives were also in self-isolation as they were showing possible symptoms. One was a student.

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Bloomfield earlier said If the student was to test positive it would be suggested that the school should be closed.

"Our advice to the school is that, if the test is positive, the school is closed over the next 48 hours as close contacts are traced ... the school would be carefully cleaned before reopening.

"We are expecting more sporadic cases of Covid-19. All our cases to date are associated with international travel ... We would expect more travellers returning to New Zealand to present with symptoms."

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The Government has suggested that any event with more than 500 people should not go ahead. Bloomfield said more advice about mass gatherings would be provided in the next day or two.

Tourist refuses to self-isolate, faces deportation

Bloomfield confirmed that a traveller who arrived in Christchurch yesterday was unwilling to commit to self-isolating and intended to continue with her travels.

The intention is now to deport her.

Jacinda Ardern on Newstalk ZB: PM looking at coronavirus 'deportation powers', warns travellers must self-isolate

He said he could understand why someone had planned a trip for a long time and then arrived at the 11th hour to find they can't travel, but said NZ authorities needed to protect people.

If someone was aware of a person who was not going to self-isolate they were encouraged to tell someone at the airport or contact Healthline or police if they were outside of the airport.

Bloomfield said there had been a big increase in cases from overseas and that meant more would be expected to return with symptoms.

Bloomfield said cost was no barrier to coronavirus testing in this country, but said the right people had to be tested. There were around 500 tests under way today.

Healthline service fielded 7,000 calls in one day

The Healthline phone service had fielded more than 7,000 calls yesterday - seven times the usual level.

He moved to reassure people that staff were doing their best to answer all calls.

There was now an online process available for those for registering for self-isolation.

Another 50 nurses have been brought in, as have additional clinical support staff from other areas to help with all of the Healthline calls.

Asked if he was satisfied with the Government's economic package today providing $500m for health spending, Bloomfield said he was "very pleased" with the amount.

Earlier today the Government unveiled a $12.1 billion support package for the New Zealand economy, with almost half of the cash to be spent on a wage subsidy package for all coronavirus-impacted businesses.

Those full-time workers eligible for the package will receive $585 per week from the Government, paid in a lump sum package of just over $7000 covering a 12-week period.

The Government is also raising benefits by $25 a week, starting April 1, and doubling the Winter Energy Payment.

This is just the first tranche of the Government spending response – the rest will be unveiled during May's "recovery" Budget.

Today's package comes as part of "the most significant peace-time economic plan in modern New Zealand history".

Focus Live: The Government has unveiled a $12.1 billion support package for the New Zealand economy.

The $12.1 billion spending package accounts for roughly 4 per cent of New Zealand's GDP and is comparatively bigger than the relief packages so far announced by Australia, the UK and the US.

"The Government is pulling out all the stops to protect the health of New Zealanders and the health of our economy," Prime Minister Jacinda Ardern said.

The big-ticket items of the package include $5.1 billion for the wage subsidy package, $2.8b for benefit increases and the bolstered Winter Energy Payment and a further $2.8b for tax changes to free up cash flow.

That's a total of $8.7 billion for businesses and jobs.

The package also contains an initial $500 million boost in health spending and an initial $600 million to support the aviation sector.

A Covid-19 sick leave scheme has also been created and will be available for eight weeks at a cost of $126.5 million.

Some 27,000 workers every two weeks are expected to take advantage of this scheme.

Finance Minister Grant Robertson said the package is one of the largest in the world on a per capita basis.

It is more than the total sum of new spending in all three of the last Budgets put together.