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A letter from the Labour leader to immigration officials on behalf of Liu was first revealed by the Herald after documents were released under the Official Information Act earlier today.
Mr Cunliffe - who said this week he had never met Donghua Liu or advocated on his behalf - told reporters he did not recall writing the letter.
He said that "I have not lied about anything to do with Mr Liu", and he would not resign.
"I did not advocate for him. A letter has just come to my attention which is eleven years old. I simply asked how long a processing process would take."
Mr Cunliffe said he still had no recollection of meeting Mr Liu.
"I simply do not recall ever having met him.
"To the best of my knowledge that letter came through my office and an immigration agent on his behalf."
Mr Cunliffe said he wrote the letter, "because it checked out on paper and it was a very low level request about how long the processing would take."
He believed he was still fit to lead the Labour Party and he had not checked as to whether he retained the support of his caucus, "because I don't believe that's necessary".
"I do not believe I have done anything wrong."
He said the situation differed from former National Government Minister Maurice Williamson's intervention with police on behalf of Mr Liu in that "Mr Williamson was guilty of intervening directly in a police operational matter".
As far as his letter on behalf of Mr Liu, "MPs do this all the time in respect of immigration cases, they simply ask how long processes take or act on behalf of their constituents as is appropriate."
"I deal with hundreds of constituents a year and this is 11 years ago. I simply do not have any recollection and nor did my office. I had asked my office to check, the advice was that we had no records.
"My memory has obviously failed me. I'm not going to blame staff, I am responsible but the advice I had was that we had no records of any meeting with Liu"
Mr Cunliffe said heads would "not necessarily roll" over the affair "my staff are long serving and well working people.
"I'm not going to be rolling the heads of my electorate office staff over something that happened 11 years ago."
He did not resile from yesterday's denials that he had ever advocated on behalf of Mr Liu.
"Do you think I would have been emphatic if I had any memory of Mr Liu? I gave you an honest answer as I recalled and I stand by that statement."
Asked how he felt today, he said: "I actually know that I've done nothing wrong so I feel totally relaxed about this."
Labour's Deputy Leader David Parker said Mr Cunliffe retained his confidence and that of Labour's caucus.
"I think David Cunliffe has told the truth at all times."
"Obviously we would rather this not have happened. David Cunliffe has done nothing he should be ashamed of here. He's told the truth throughout."
Labour MP Trevor Mallard, when asked whether Mr Cunliffe retained the confidence of caucus replied, "David Cunliffe is the Leader of the Labour Party".
"I've always been loyal to the Leader of the Labour Party."
National: Cunliffe must explain
Prime Minister John Key told nzherald.co.nz in New York that "politics is all about trust."
"Mr Cunliffe has asked New Zealanders to trust him that he has had no involvement with Donghua Liu and yet this letter suggests the opposite.
"Quite clearly he will need to explain his actions."
Asked if he thought it was more likely to be a mistake than a lie he said "i wouldnt want to speculate on that."
"But there have been a number of occasions in the past where getting to the truth of matters has proven quite challenging for Mr Cunliffe."
He would not speculate on whether the revelation would put pressure on Mr Cunliffe's leadership.
Acting Prime Minister Bill English said the revelations were "a real surprise" because Mr Liu's donations and connections to MPs had been debated in Parliament for two months.
He said the new details would make it difficult for the public to take Mr Cunliffe at his word.
"He has got a lot of explaining to do," Mr English said. "His credibility on these issues was pretty thin anyway. He set up his own personal trust and won't reveal the donors to it in the way everyone else has to. Now this really blows his credibility to bits."
Mr English said he did not remember every letter he wrote in 2003, but added: "If there was a couple of months of public discussion about a high-profile donor that I knew I would go to the trouble of finding out."
Economic Development Minister Steven Joyce said Mr Cunliffe had "a real problem".
"If this is the sort of standard he wants to take to the election campaign then I think it's something that I think the public of New Zealand will be very interested in.
"He's basically saying it doesn't matter that I say to you one day one thing and the next day that it's something completely different in fact the exact opposite."
Asked whether he believed Mr Cunliffe had lied, Mr Joyce said: "He's got to square this particular circle, I don't believe he can."
"The Labour Party needs to absolutely come clean about everything else they've talked about Donghua Liu that weirdly they don't know anything about."
Mr Cunliffe said the criticism that he had betrayed the trust of New Zealanders was "politics as usual".
Mr Cunliffe said his office dealt with "hundreds and hundreds of constituents every year that since 11 years ago adds up to thousands".
"My office it now appears was approached by an immigration agent on his behalf and on that basis I agreed to write a low level process inquiry, it is not a substantive advocacy for his case."
"I did not tell a lie, I absolutely did not. I did not intervene in support of his application."
The forgotten letter
The 2003 letter was written in his capacity as the MP for New Lynn after he was "approached my constituent Donghua Lui [sic] who is concerned at the time it is taking to process his Investment Category application".
Mr Cunliffe this week denied any involvement with Liu's residency bid after the Herald revealed the property developer paid $15,000 at a Labour Party fundraiser for a book signed by Helen Clark in 2007.
The letter, released to the Herald today under the Official Information Act, dated April 11, 2003 said Liu's application for residency was accepted for processing by the Immigration Service on August 13, 2002.
Mr Cunliffe said Mr Liu wished to set up a joint venture business with his Tianlong Property Development Company - which owns his stalled property development in Newmarket - to export large quantities of agricultural and horticultural products to China.
"It is hoped that products from the company will be available to the market in July 2003," wrote Mr Cunliffe.
"I am aware of the difficulties facing the Business Migration Branch of New Zealand Immigration Services in coping with the overwhelming numbers of applicants that have applied for consideration under these categories and the time taken to verify documents.
"However, it would be very helpful to Mr Liu to be advised of an estimated period of time in which he could expect a decision on his case."
Yesterday, Mr Cunliffe told reporters questioning him about Liu's financial support for Labour he did not recall meeting him and denied advocating on Liu's behalf in his residency application.
Liu was granted residency under the Investor Category in 2005 by Labour's associate Immigration Minister Damien O'Connor against official advice.
The Herald this week revealed Liu's $15,000 secret donation to Labour and today published a 2007 photograph of Labour MP Rick Barker, the Internal Affairs Minister at the time, presenting a bottle of wine to Liu's partner at another Labour Party fundraiser.
Mr Barker also visited Liu in his hometown of Chongqing for a lavish dinner that year.
The Labour Party has previously accused the National government of making "cash for access" deals with Liu, who received citizenship in 2010 after lobbying from National minister Maurice Williamson and whose hotel was later opened by Prime Minister John Key.
He gave $22,000 to the National Party in 2012 through one of his companies, and had meetings with Immigration Minister Michael Woodhouse in an attempt to secure relaxed immigration rules for rich migrants.
Mr Williamson quit his ministerial portfolios last month after the Herald revealed he contacted police over a prosecution against Liu.
David Cunliffe to reporters yesterday
Q: Do you recall ever meeting Liu?
A: I don't recall ever meeting him, no.
Q: Did you have anything to do with the granting of his permanent residency?
A: No, I did not.
Q: Did you advocate on his behalf at all?
Q:Were you aware of any advice against granting him permanent residency?
A: Not to my recollection.
- by Adam Bennett, NZ Herald