ActionStation said it chose the Advocate because it covers the electorate where Mr Peters lives.
The letter lists four objectives - a well-funded public health system, world-class education and training for youth, trade deals that put New Zealanders first, and "making media and public broadcasting great again" - which were all policies or election promises made by Labour, the Greens and NZ First, but were not, according to the group, a top priority for National.
Campaign director Laura O'Connell Rapira (Ngapuhi, Te Rarawa) said the group normally campaigned for policies, not parties, so made sure it had a mandate from its members before running the ad.
Immediately after the election the group surveyed its recently active members about which party or parties Mr Peters should go into coalition with. Of the 4000 responses received 92 per cent wanted a Labour-Green-NZ First coalition, she said.
Ms O'Connell Rapira conceded that an ad on its own would not be enough to sway Mr Peters. The group was also asking the 11 per cent of its members who had voted NZ First to contact the party directly and express their views.
Mr Peters, whose party holds the balance of power, has been coy about his preferred choice of coalition partner.
He has also stated he won't start negotiations in earnest until the final election results are released this Saturday. The results so far do not include special votes cast overseas or by people who enrolled on the day they voted.
The election night results give National 58 seats, Labour 45, NZ First 9, Greens 7 and Act 1, though those numbers could still change. A minimum of 61 is needed to form a government.
Mr Peters declined to comment on the ad.
Other ActionStation campaigns in the past year include calling for an inquiry into mental health services, equal pay for female workers, an increased refugee quota, an end to tax-dodging by multinational firms, and an investigation of the Saudi sheep deal.