More than 100 extra staff have been called into Telecom for a second day to deal with call volumes after 60,000 customers had their passwords cancelled over the weekend.
Telecom cancelled the passwords of more than 15 per cent of its 450,000 customers on Saturday night without warning.
Users unable to log on had to change their passwords by answering a number of security questions.
Once they were into their email account, a message from Telecom told them: "We have cancelled your current password and you will need to, or have had to, change your password immediately to use your email account."
Thousands of customers are still reportedly without access to their accounts.
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Despite extra staff called in at the last minute to cope with calls, users were facing wait times of up to an hour and a half as they tried to get their password changed.
The call centre fielded more than 3000 calls from people asking for help.
Head of external media at Telecom, Jo Jalfron, said 107 extra staff had been called in again today.
"Some of them were already doing double shifts. Some of them had already been working 12 hour days," she said.
While wait times for Telecom's main broadband queue remain long, "additional resourcing" had reduced waiting times to around five minutes, she said.
Customers are angry Telecom didn't advise them of the change, pointing out that the email letting them know came after access to their email had been blocked.
"It would have been good to receive the email advising that account access was to be blocked beforehand, or a message on our landline which is also Telecom," said Glenda Baillie. "Unimpressed."
Others said changing their password had been futile.
"Within 10 minutes of changing my password, changing passwords on other internet sites, I logged onto my extra emails and guess what .... another spam email," said Liz Mills.
"Clearly the issues that Telecom are having are not yet rectified."
Telecom has advised customers to change their password since last weekend's cyber-attack.
Despite contention over whether password changes helped to fix the problem, Telecom stood by its actions and urged customers to be patient.
"We're asking customers that do need to call us, to be please be patient given the magnitude of this issue and the resulting high call volume," said Telecom general manager Trish Keith.
"We're hugely sorry for the inconvenience this situation is causing our customers and trying our best to assist them both through our call centres but also through email information and social media."
People must not only change their passwords on their computers, but on their mobile devices too, Telecom said.
Close to 110,000 people have now changed their passwords.