Earthquake Commission chief executive Ian Simpson offered his resignation to Earthquake Recovery Minister Gerry Brownlee during a meeting on a privacy breach.
The EQC has had to apologise twice for accidentally emailing information about 83,000 Canterbury earthquake claimants to someone outside the organisation.
Mr Simpson said the minister told him at a Beehive meeting on Tuesday that he should focus on the job at hand and make sure any problems or errors are not repeated.
The chief executive said they discussed further steps the commission could take to avoid a repetition of the breach, and a technical review will cover how the original error occurred and what measures can be taken to prevent a recurrence.
Mr Brownlee told reporters he had confidence in Mr Simpson. "He understood that it had caused embarrassment to the Government and said that if he was a casualty of that, he certainly understood that. I said, look, we've got a problem that we've got to get over."
Labour Party leader David Shearer says the Government is treating the issue too lightly. "There needs to be a process in place by which this cannot happen and the Government has not put out any sort of safeguards to enable that process to occur."
An Excel spreadsheet containing claim details of clients in EQC's Canterbury Home Repair programme accidentally sent by a staff member to the wrong email address contained information regarding building quotes, estimated settlement costs and details of cash settlements.
Earlier on Tuesday Mr Simpson told Radio New Zealand's Morning Report programme that corrections had been made to email systems to make sure this would not happen again. Changes included not sending out spreadsheets as email attachments.
Files contained 'many details'
The information was mistakenly sent to Bryan Staples, chief executive of insurance advocacy company Earthquake Services, last week.
Mr Staples said the attachment was full of details Cantabrians have been asking the EQC to provide for over two years, including estimated settlement costs and the number of cash settlements the commission is expecting to make.
"I saw that over 60,000 of those claims were categorised under $50,000. This is absolutely outrageous - it's political. EQC fixing Christchurch is all about the next election. They're going to try and cash settle claims for under $50,000. They need to come clean."
The attachment contained EQC estimates of repair costs but Mr Brownlee said that cannot be given to claimants themselves because it is commercially sensitive.
"Obviously we want tradespeople who are doing that work to compete for the work," he said. "If you say right up front what you expect to pay you'll end up paying more, and that would come out of the pockets of taxpayers."
Mr Staples has deleted the email and and promised the information would not be distributed any further.
He said the EQC staff member who sent the file was someone he is in regular contact with and he told her about it within half an hour of receiving the email.
Mr Staples is adamant it was not him who passed information to Ms Dalziel and said he was disgusted politicians had turned turned a simple human error into a political football.