Reserve Bank head of communications Mike Hannah said the bank was "aware of the issues that occurred overnight and we're monitoring it."
Some bank customers were left with no money to buy school lunches and petrol, and may face overdraft fees.
Shannelle Cooke, from Kumeu, said she had no petrol in the car to get to work, and no money to buy it after wages failed to go through overnight.
But she said payments scheduled to go out of her account were still processed.
"I couldn't buy bread to make my son's sandwiches for lunch. I had to borrow money to get to work."
She said her account was now in overdraft, and she hadn't received any assurances from ANZ over whether she would be charged fees.
"It's really frustrating considering when they want money from me they hound me, but when I'm waiting for money from them, I'm expected to just deal with it."
Another ANZ customer said she was told overdraft fees would be charged, and customers would have to ask for a refund.
Liz McGuire said she was told by the ANZ helpline that fees would be automatically applied, but if asked the bank would "maybe look at" reversing them.
"If it is a bank error then they would get more kudos by not charging the overdraft fee in the first place."
Tauranga woman Tracy Brownie said she was also unable to buy lunch-box food for her children after her Westpac eftpos card was declined at 7am.
"It was most embarrassing because I knew my pay should have been in there," she said.
She checked her accounts and found ANZ payments had gone through, and was able to buy lunches from that account.
About 9am she said payments were now showing up in her Westpac account. " Not good enough really is it when we get charged so much by the bank."
Another Westpac customer, Johnny Long, said his entire long-weekend takings of about $20,000 had not gone into an account.
On Twitter, Merja Myllylahti wrote: "No salary to day, thanks to ANZ. No payments at the AUT." She updated at 10am to say the money had gone through.
Scott Muir tweeted: "ANZ - what a joke, "exceeding expectations" on profit and screwing up payments less than 24 hours later...".
A spokeswoman for BNZ said a technical problem with one of the banks had produced a knock-on effect which delayed payments across the sector.
"A technical issue at one of the other banks has meant that many of the banks couldn't produce payments at the usual time, which is about 1am,'' she said.
"We started processing payments about 4am, so we have about a three-and-a-half hour delay.''
She said the bank was working "really hard'' to get all customers paid as quickly as possible, which would "hopefully [be] later this morning''.
"No customers will be out of pocket from the glitch,'' she said.
"Everyone will get paid, and if there's any problem then customers can give us a call.''
This is not the first time ANZ's network has been hit by a glitch this year:
ANZ internet banking glitch resolved
Eftpos glitches not due to National merger - ANZ
ANZ customers affected by outages
ANZ network hit by nationwide fault
ANZ network hit by nationwide fault
After last year's outage, the Reserve Bank said Payments NZ had taken steps to better manage or avoid similar incidents. The central bank was continuing to monitor risks to the retail payments system, it said at the time.
In March of this year, the central bank released a consultation document, Strengthening Statutory Payment Oversight Powers.
Among responses was the suggestion that Payments NZ be formally recognised as a co-regulator for payment systems oversight. The central bank didn't agree, responding that as the body was owned and advocated for participants in the industry being regulated, it was not appropriate that Payments NZ be positioned as a co-regulator.
The Reserve Bank is currently working on proposals to feed into a Cabinet paper of its preferred policy position on a payment oversight framework, and expects to have a draft ready for consultation in the first half of 2014, it said this month.
Nichols said Payments NZ coordinates an industry group that is called up in the event of outages, such as happened overnight. The Reserve Bank's proposals to strengthen its oversight "do not in any way diminish the responsibilities we have," he said.
While there was still debate over the central bank's plans, the way it had been presented to industry "seems quite reasonable," he said.
- with Heather McCracken/APNZ
