Speaking to media this afternoon, Ardern did not rule out a ban on travellers coming in from Europe - as President Donald Trump announced for travellers into the US yesterday.
She also did not rule out restrictions for people coming from the US where the outbreak has also been escalated with more than 1000 infected and 41 deaths.
"We have to be concerned where we've seen outbreaks in any part of the globe."
Current travel restrictions in New Zealand include a ban on foreigners coming to New Zealand from China and Iran.
And people coming from Italy and South Korea have to self-isolate for 14 days, while health officials have been empowered to quarantine cruise ships and planes, if necessary.
But there are issues which need to be worked through with the special Covid-19 subcommittee over the weekend about further restrictions, she said.
For example, some medications come into New Zealand on passenger flights so the Government needed to ensure access to those wasn't cut off.
There are also likely to be restrictions on travel from New Zealand to the Pacific.
Given the recent measles outbreak in Samoa and New Zealand has a responsibility as the "gateway to the Pacific" to do all it can to prevent transmission of Covid-19 to those nations, Arden said.
"We are exploring what would have some impact, what could have some effect, what could provide potentially an extra layer of protection.
"We take very seriously our duty of care."
This was among the reasons the Pasifika Festival in Auckland at the weekend has now been cancelled.
About 60,000 people were expected to attend over the two days with many flying in from the Pacific for the festival.
Ardern said this would affect the ability to contact-trace and treat possible cases within our healthcare system if they then returned home.
And being held in Auckland, it was closer to the confirmed cases, and the Pacific had its first confirmed case in the last 36 hours, Ardern said.
Tahitian parliamentarian Maina Sage, who returned from Paris at the weekend, tested positive for Covid-19 yesterday.
"Those special circumstances meant there was extraordinary discomfort around going ahead with Pasifika," Arden said today.
Earlier, Ardern said the memorial to mark the one-year anniversary of the March 15 attacks will go ahead despite Pasifika being cancelled during the coronavirus pandemic.
She acknowledged that could change in the next 24 hours if advice changes, as it did with the Pasifika Festival.
Ardern confirmed there will be more cases of Covid-19 in New Zealand.
The Government is working to flatten the curve of the infection rate of the virus.
"We will see cases, the goal is to slow those cases.
"[To] make sure we can contact-trace every case we have and we can constantly provide the medical treatment that may be required to measure this global pandemic."
Asked why the Government isn't temperature testing at the airport, Ardern said the issue was that doing so only picked up people with symptoms and that could lead to a false sense of security.
There was a concern this would lead people to be lenient with self-isolation if they'd come from an affected country but didn't have a temperature.
Ardern once again urged anyone who felt sick to stay home.
Earlier today, Finance Minister Grant Robertson cancelled his travel to Australia today to meet his counterpart Josh Frydenberg, opting instead to meet Treasury officials this morning and to Skype with Frydenberg later today.
Robertson has previously outlined three scenarios that Treasury officials were working through, including the possibility of a recession in New Zealand and a worst-case scenario of a global recession.
The Government has introduced a number of measures to combat the economic fallout of the spread of Covid-19 and will announce details of its targeted business continuity package on Monday.
The business community and the Opposition has been pressuring the Government to do more.
Meanwhile, the Director-General of Health Dr Ashley Bloomfield has reminded people to ring Healthline on the dedicated Covid-19 number: 0800 358 5453 or ring ahead to their general practice if they are feeling unwell, and they'll be advised what to do.
Aged care facilities have been advised to ramp up their communications with visiting friends and relatives to warn anyone sick with coughs, colds or flu to stay away.
"Our key advice, which is fundamental to our response, is not putting yourself or others at risk if you are unwell," Bloomfield said.
"This means not going to work or going to places where there are other people if you are sick. All of us have a role to play in stopping further spread.
"I need to emphasise how critical this is as New Zealand responds to Covid-19.
"This is particularly important for concerts and other large gatherings we have coming up, including this weekend.
The World Health Organisation declared a pandemic yesterday as the number of people with the virus surpassed 120,000 worldwide, while global markets crashed after US President Donald Trump announced a ban on travel between Europe and the US, a move condemned by the EU.
