A four-hour special was being run on Monday, with fares beginning at $9. Normal fares would start between $45 and $49.
Jetstar's website appeared to be struggling to handle the volume of traffic from visitors checking out its new services, returning blank pages or loading slowly.
Jetstar New Zealand boss Grant Kerr said it was "fantastic" the site had crashed, because it showed how much interest there was.
Staff were working to fix the problem and Jetstar would consider extending the four-hour special window.
As people vented their frustration on social media, spokesman Phil Boeyen said the problems appeared to be simply due to the volume of traffic to the site.
"It is great to know that it is that popular," he said.
All routes will fly between the regions and Auckland, with the Nelson flights also going to Wellington. All rates were now on sale, and the first flights - from Nelson and Napier to Auckland - will begin in December.
The low-cost airline chose the destinations from a longlist of Hamilton, Rotorua, Tauranga, New Plymouth, Napier, Palmerston North, Nelson and Invercargill.
Nelson was the big winner as it was the only centre with two destinations - Wellington and Auckland.
Nelson Mayor Rachel Reese said she had kept the announcement secret for 36 hours.
"You can hear the people cheering from Trafalgar St," she told the crowd at Wellington Airport.
Wellington Mayor Celia Wade-Brown said the news meant there was now more reason to extend Wellington's runway.
It meant people from the top of the South Island now had more opportunity to fly to Wellington then elsewhere overseas. A longer runway would mean more options, she said.
Nelson MP Nick Smith said it was "fantastic news" for Nelson, an isolated region that depended on the strengths of its links with other parts of New Zealand.
"Studies show that on average air fares are 30 per cent less where there is effective competition and that amounts to millions of dollars of savings and thousands more visitors to Nelson."
Smith said the Jetstar link was important to the visitor industry, but the biggest gain for Nelson was making nationwide businesses viable in Nelson and for people to be able to easily connect across the country through more competitive air services.
"With house prices going through the roof in Auckland there is an opportunity for us to attract businesses to our region."
He was "pretty loyal" to Air New Zealand, a good company that deserved credit for its substantial investment in maintenance services in Nelson.
"But I still believe the region's overall benefit is in having a choice of services," Smith said.
Nelson Tasman Tourism chief executive Lynda Keene said the increased competition was "really great news" for Nelson and Tasman residents.
"Grandparents who might go to Dunedin, Auckland or Christchurch once a year might be able to travel three or four times a year. It's definitely going to open up a lot more opportunities."
It was also really exciting from a business perspective, she said.
"We're really fortunate to have a lot of frequency with Air New Zealand which has been a wonderful contributor to the region, but Jetstar coming in is going to make it a bit easier for people coming out of Auckland, Wellington or Christchurch, particularly for trans-Tasman services."
It would also make international travel more accessible through Jetstar's links with Emirates.
With Originair and Kiwi Regional Airlines joining the regional competition, "it's raining planes", Keene said.
Palmerston North mayor Grant Smith said the announcement was welcome for the city and the region.
"It's only good news," he said.
"The region will get lower fares and it will also help people who otherwise couldn't travel.
"There is choice there for them," he said.
Smith expected the move to give tourism in the region a boost and help retailers and agribusiness as well.
"It will bring more travellers to the region," he said.
"Attractions like the [Manawatu] Gorge and the Tui brewery will become more accessible."
New Plymouth Mayor Andrew Judd said Jetstar's decision was great news for the people of in the region.
"Having both Air New Zealand and Jetstar operating out of New Plymouth will give passengers more choice and more opportunity to afford to fly, and give visitors even more reasons to come here," Judd said.
The New Plymouth District Council was already planning extensions at the airport's terminal, runway apron and public car park, with construction due to start in May next year.
Some southern leaders were disappointed Invercargill was not a new destination.
Southland District Mayor Gary Tong said he was not involved in the consultation with Jetstar, and it was disappointing they had chosen not to come.
But he was hopeful Jetstar would consider Invercargill again.
"There are certainly the numbers [of people] coming south."
Venture Southland chief executive Paul Casson said although it was disappointing, other airlines might be interested.
"Visitor numbers look good for the next few months... there may be other airlines who want to fly into our region."
Jetstar had made a commercial decision to support smaller regions than Southland, he said.
"Luckily we've got Air New Zealand, and they're very good to us, which we've seen last week in a reduction of fares."
'Very competitive process'
Economic Development Minister Steven Joyce and Transport Minister Simon Bridges welcomed increased competition in the regional aviation market.
Transport linkages are crucial for regional development and these new air linkages will help boost business and tourism traffic into regions like Taranaki, Hawke's Bay, Nelson and Manawatu/Whanganui," Joyce said.
"I know it's been a very competitive process between the different regions for the opportunity to host the new carrier. I'm confident that this expansion of regional routes will be successful and lead to more competition on regional routes in the future," he said.
The first of Jetstar's fleet of five regional 50-seat Bombardier Q300 aircraft to service the routes arrived in Wellington over the weekend.
Jetstar will face stiff competition from national airline Air New Zealand, which announced last week that it will slash two million flights to below $100 over the next year.
The announcement came as Air New Zealand celebrated record profits of $327 million in the year to June 30.
Air NZ chief executive Christopher Luxon said lower fuel prices and more seats would drive down costs for fliers.
House of Travel commercial planning director Brent Thomas said competition from Jetstar also played a part.
"The competitive landscape of airlines means the lower cost gets passed through to consumers relatively quickly once the hedging comes off, " he said.
TOM HUNT, GREER BERRY, BILL MOORE AND BLANTON SMITH
Last updated 10:37, August 31 2015