Spark is asking people to use internet apps like Apple Facetime to contact each other as overloading continues to plague the traditional phone systems.
"Following the Prime Minister's Covid-19 announcement today telecommunications providers experienced call volumes beyond any level of calling ever seen in New Zealand to date," The company said in a statement.
"This is creating significant congestion for voice calling at an industry-wide level.
"We are working collaboratively to rectify the issue with urgency."
Those who could get through complained about call quality. "[It's] like calling Mars," quipped Francis Till.
The telco also updated on its website and social media late this afternoon: "Customers may be experiencing a loss of service for voice calling. The New Zealand telecommunications industry is working quickly and collaboratively to remedy calling issues that have stemmed from a significant increase in voice volumes on both mobiles and landlines. New Zealanders are encouraged to use internet-based calling options such as Skype or Facetime until this issue is fixed."
Anecdotal evidence suggested broadband was holding up while traditional phone services fell over. Network operator Chorus said there was no congestion on its fixed-line broadband network.
"The data and voice networks are separate and people are encouraged to use messaging apps to keep in touch," said Geoff Thorn, head of the Telecommunications Forum, an industry coordination body that counts Spark, Vodafone, 2degrees and Chorus among its members.
"The industry is working together to resolve the issues of congestion due to an increase in calling volume in the order of 350%," Thorn said.
This morning, numerous readers reported a "Your call cannot proceed at this time due to congestion" message when they attempted to use the phone amid a surge from working from home - and then another surge in calling as the upgrade to Level 3 was announced mid afternoon.
Vodafone has been the first telco to respond, with a spokeswoman telling the Herald, "Voice call volumes are up approximately 20 per cent as more Kiwis are working remotely.
"Today's issue is impacting the full industry and we're fixing it as a matter of priority, which includes working with other telcos on call interconnects.
"There has also been a spike in suspected spam calls from overseas numbers, which we're working to block."
As the TCF and telcos work to resolve the issue, users have taken to social media to vent.
After this reporter tweeted about not being able to reach a landline in Whanganui, many got in touch saying they had experienced the same problem with attempted calls on, variously, Spark, Vodafone, 2degrees and Spark-owned Skinny.
"Trying to call a landline from my mobile and repeatedly getting a 'Your call cannot proceed at this time due to congestion.' ... People trying to call me not connecting. I'm with @vodafoneNZ," said NZTE marketing manager Amanda Pausina.
Enterprise architect Mark Heseltine said, "Same here, on Skinny mobile, trying call to @2degreesmobile."
And Mike said, "Seems the 2degrees network is having major issues.. you can call other 2degrees numbers but when anyone calls them or they call - they get a 'you cannot be connected'."