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Labour Party finance spokesman David Cunliffe said the resignation added to unanswered questions following Mr English's "blunder" last Friday about selling the bank.
"Sam Knowles has done a magnificent job setting up Kiwibank.
"His resignation is a huge loss and couldn't be worse timing for the Government given the uncertainty Bill English has created around the bank's future."
The gaffe by Mr English on Friday to a post-Budget audience in Christchurch about what he really wanted to do with Kiwibank had sent Prime Minister John Key into hasty damage control and had outraged many of Kiwibank's 700,000 loyal customers, Mr Cunliffe said.
The economics of retaining Kiwibank in public ownership were compelling.
The bank had played a major role in improving the competitiveness of the banking industry as far as New Zealanders were concerned, he said.
Mr Knowles announced to the market that he would be resigning after 10 years involvement in setting up and then leading the bank.
Chairman Jim Bolger said Mr Knowles had changed the face of New Zealand's banking industry for ever.
"Sam's resignation is a huge loss for Kiwibank but he has set up a strong, robust company that will continue to go from strength to strength.
Sam's impact on the New Zealand banking industry has been immense," Mr Bolger said.
Kiwibank is owned by New Zealand Post whose chief executive Brian Roche said a search both internally and externally would begin immediately for a replacement for Mr Knowles.
Mr Cunliffe wanted to know what communication there had been between the Government and the boards and management of New Zealand Post and Kiwibank over recent months and how Mr Knowles felt when Kiwibank's request for a Crown capital injection was turned down earlier this year.
"The Government also has a potential governance issue on its hands now as it tries to dig itself out the public relations and economic hole it has dug itself into the past week."
However, Mr Knowles told a news conference that his departure had nothing to do with what the Government was talking about, nothing to do with board issues or the recently-arrived Mr Roche.
He was in good health and had not had a job offer from Australia.
"The reason I'm leaving Kiwibank is because it's the right time to leave Kiwibank and it's the right time for a number of reasons."
Those reasons included that the bank had proved itself by coming through the recession.
Kiwibank had delivered well beyond its business case put in place 10 years ago and now a new business case, for the next decade, had been developed and put to the Government.
"I think it's the right time for me to stand back and someone else to look at the next 10 years," he said.
Mr Knowles also believed that keeping New Zealand control of Kiwibank was part of its value.
NZ Post company secretary Malcolm Shaw confirmed in a statement that the postal group had been in discussions with the Government concerning a range of support options that various long-term growth strategies for Kiwibank might require.
"These discussions have not reached any conclusion, and are ongoing," he said.
Later, Mr Bolger said he expected to be replaced as chairman later this year, when his term expired, by former Labour finance minister Dr Michael Cullen.