The bank's Facebook page has been flooded with people complaining about the issues.
One woman said she couldn't get cash out of an ATM while another said she was unable to buy groceries due to the problems.
"I went to transfer money over but bank app is still down went in sat in the line at paken save [Pak'nSave] to do all shopping yet couldn't transfer my money over terrible Kiwibank."
Another woman complained of not being able to get access to bank statements which she needed to send to her auditor urgently.
One man said he had tried to get through to the call centre but had been cut off six times.
"I waited for over an hour on the phone to speak to someone and gave up!!! SLACK!! (after being cut off six times trying to call you!)"
But others urged people to calm down and give the bank a chance to fix the issue.
A Kiwibank spokeswoman said it was having intermittent issues with some services including internet banking, app, website and phone services.
Asked if the bank had been subject to a cyber security attack or Distributed Denial of Service (DDoS) attack the spokeswoman said it had identified the cause and was working hard to fix the issue.
She did not say what the cause was.
"Our priority at the moment is continuity of service for our customers. We apologise to our customers for any inconvenience caused and thank them for their patience and support."
In a DDoS attack the hackers overwhelm a site with thousands or millions of bots trying to connect to it at once, rendering it inaccessible. There's no element of breaking into servers or stealing data.
On Friday afternoon Voucs, which owns Orcon, Slingshot, Flip, and Stuff Fibre suffered anoutage that left customers without access to the internet.
Vocus said today that Kiwibank was not the Vocus customer targeted by its DDoS attack three days ago.
"Friday's attack was on a customer, not on the Vocus network," a Vocus spokesman said.
"The Vocus network wasn't under attack then, and it isn't now."
On Friday, "A Vocus customer was under DDoS attack this afternoon. A DDoS mitigation rule was updated to our Arbor DDoS platform to block the attack for the end customer. Based on initial investigations it was this rule change that disrupted service to a range of Vocus customers. We are working closely with the vendor of this platform to understand why this occurred," the Vocus spokesman said.
