The court will hear arguments on Tuesday on whether the conversation was illegally recorded.
Ambrose has asked for a declaration on whether the conversation was a private communication. If not, his recording was not illegal.
The letter sent to Mr Key's lawyer yesterday claims Ambrose has been publicly accused of "criminal conduct, unethical journalism and dishonesty", that his actions have been compared to the "notorious phone hacking undertaken by the News of the World", and that "his integrity has been directly impugned in a very public matter by very senior members of the Government".
"Over the last week, members of the National Party, and in particular Mr Key and Mr Joyce, have made a number of public statements about Mr Ambrose and his conduct," the letter says.
"To mitigate the damage done to Mr Ambrose, it is appropriate that the retraction and apology occur without delay."
A Government spokesman said the letter had been received.
"The matter is in the hands of the National Party's lawyers, and there is no further comment."
The letter notes that Ambrose has always been a National Party voter, and also asks for all documents relevant to allegedly defamatory comments - including the motivation for making them - to be kept.
Last night, several media outlets received police search warrants to be executed within the next month.
The warrants cover Radio New Zealand, TVNZ, TV3 and the New Zealand Herald premises, which include the Herald, the Herald on Sunday and the Herald Online.
Meanwhile, a One News-Colmar-Brunton poll indicates Epsom voters have largely ignored Mr Key's public endorsement of Mr Banks.
The poll asked 517 Epsom voters who would get their vote as electorate MP.
Mr Banks received 30 per cent support, behind National's Paul Goldsmith on 41 per cent.
Labour's David Parker was on 17 per cent and the Greens' David Hay on 11 per cent.
Act is polling well short of the 5 per cent MMP threshold, so would not return to Parliament unless Mr Banks can win Epsom.
The survival of Act, even if it has only two MPs, could be critical in National forming a centre-right coalition if it fell short of enough votes to govern on its own and New Zealand First returned to Parliament.
NZ First had 4.9 per cent support in this week's Herald-DigiPoll survey.
Mr Banks is alleged to have called Dr Brash a "strange fellow" on the teapot tape and discussed Catherine Isaac - No 2 on the party list - as a future party leader.
Dr Brash told the Weekend Herald he did not consider being called "strange" an insult.
"I've been called a lot worse things. Some people might think that someone who left the Reserve Bank Governor's position to go into Parliament was, by definition, strange."
But he did not regard himself as strange. He also considered Ms Isaac to be a potential leader.
Status updates
* TVNZ, Radio New Zealand, TV3, the Herald on Sunday and the Herald have received notices of police search warrants for material relating to the cameraman Bradley Ambrose and the "teapot tape" - to be carried out in the next month.
* A High Court hearing has been set down for Tuesday to consider arguments about whether the "teapot tape" was illegally recorded.
