"They said the breach wasn't a problem, really, it was just a third party using information."
Barton said it sounded like the ministry was trying to downplay the mistake and was looking after the organisation "more so than looking after me".
"Breaches of privacy are obviously quite serious.
"This is the Government we're talking about. They should know the laws more than anybody about privacy and making sure information is secure."
He said it was "unsettling" to think that copies of his birth certificate and driver's licence could be in the hands of fraudsters.
"I don't know how many people, or who, or where my information has gone," Barton said.
"My trust levels for giving anything to the Government now are pretty low.
"Somebody has to be held to account for this."
The ministry had not advised him what steps he could take to protect himself, he said.
"Basically, all they've asked me to do is respond to an email ... and give them consent to work on my behalf."
Speaking at a media conference on Sunday, the ministry's chief executive Bernadette Cavanagh said her "number one focus" was providing support to those affected.
"We're taking whatever measures we possibly can, whether that be giving them new documents, new passports, new drivers' licences.
"And also trying to provide support and advice ... that they might be able to take to be a bit more sensitive and cautious now that their information has been unfortunately published."
All those affected had been offered replacement documents free of charge, Cavanagh said.
She would be launching an "external review" to see what went wrong and to ensure the ministry's security processes were robust, she said.
National MP Nicky Wagner told RNZ the error appeared to be "a mixture of carelessness and naivety".
She said the public's faith in the Government's ability to keep information safe would be disappearing fast.
"I have no confidence and I can't expect the public to have confidence. This is appalling."
The Government's chief digital officer, Paul James, acknowledged the error would dent public trust.
"Every day, government holds, protects, transacts millions and millions and millions of pieces of personal information and does so safely and securely.
"However, when we don't get it right, it clearly has an impact on trust and confidence."
James said he would write to all public chief executives to remind them of the required standards and to confirm they were complying.
- RNZ
