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The email also states that Mr Banks suggested Dotcom's staff met Prime Minister John Key personally to try to smooth the red tape around his mansion purchase.
The email was written to Dotcom by his head of security, Wayne Tempero, on July 30 just after taking a call from Mr Banks.
It comes amid a police investigation into three political donations made to Mr Banks' 2010 mayoral campaign. The three anonymous donations included one from Dotcom, who said he made a $50,000 donation to the campaign split into two payments at the request of Mr Banks, who says he followed the law.
Dotcom, under house arrest resisting extradition to the US on internet piracy charges he denies, has also offered an explanation why he decided to release information which proved so damaging for Mr Banks.
Mr Tempero, who has acted as a bodyguard for David Beckham and Michael Jackson, wrote to Dotcom: "I just had a call from John Banks about asking you for a small donation for the Act Party which he is standing for government this year.''
The email was sent immediately after Mr Tempero spoke with Mr Banks at about 8pm.
Mr Tempero also wrote that Mr Banks said "he will be a very good friend for you when he is in Parliament''. He said Mr Banks had spoken of being "personally embarrassed'' that Dotcom was unable to buy the north of Auckland mansion he was living in.
Permission to buy the $30 million property was declined in July by Lands Minister Maurice Williamson, who initially approved the deal, and Justice Minister Simon Power.
Mr Banks had lobbied Mr Williamson on Dotcom's behalf.
According to Mr Tempero's email, Mr Banks said "once in government'' he "would have the power to do something about it''.
Mr Tempero said Mr Banks had suggested a personal meeting between the Prime Minister and the bodyguard. He said it would give the opportunity to explain Dotcom's current and future efforts for New Zealand and "Banks thinks the PM will intervene''.
In an emailed statement, Mr Banks confirmed asking for money.
He said: "I do recall raising the issue of donating to the Act Party with Mr Dotcom's staff ... I was subsequently advised by one of his staff that Mr Dotcom said `to go get f****d as your Government has caused me too much trouble' or something along those lines.''
He said he had already stated he had briefed Dotcom on the Overseas Investment Office application.
Asked about Mr Tempero's other comments, Mr Banks said, through a spokeswoman: "Mr Tempero's recollection of events is different to mine. I will not be responding to any further allegations made by Mr Tempero.''
In a second email to Dotcom after the November election, Mr Tempero said he had another call from Mr Banks looking for a hotel recommendation in Hong Kong, where he was travelling for a Christmas holiday.
"He [said he] would like to sit down with you in the new year to talk about how he can be a service to [you] and the family now [he] is back as an MP.''
Mr Key said he had not been asked by Mr Banks to meet any Act supporters. Asked if he would speak to Mr Banks about the donation claim, he said: "No, this is a matter for Act.''
Dotcom said he did not donate money to Act. He said the request came just as he was learning the application to buy the mansion had been rejected.
Dotcom said he was also disappointed in Mr Banks' representation of his electorate. He had a "particularly uncomfortable'' time in prison because he had to sleep on a steel bench with a thin mattress while dealing with the pain of two slipped discs.
He said he asked his lawyers to contact the local MP, Mr Banks, to raise awareness of conditions in the prison.
He said Mr Banks, who had professed friendship less than a month earlier, had asked through his staff for Dotcom not to make another request.
- David Fisher of the New Zealand Herald