In a congratulatory letter sent last week, Puna described the event as a “... tremendous achievement by the NZ Government team” and praised the efforts of NZ Foreign Minister Murray McCully and Ambassador Jim McLay in New York.
Last Thursday, New Zealand secured enough votes to win a seat on the Council as a non-permanent member.
Four other countries won a seat, including Spain, Angola, Malaysia and Venezuela.
In the vote, NZ picked up 145 votes, claiming one of the "Western Europe" and "Other nations" seats, ahead of Turkey and Spain in the first round of voting.
In the aftermath of the victory, Key told reporters NZ would be a "small country with a loud voice", while McCully issued public comments saying his country will work towards reforming the council.
New Zealand will hold the seat for two years, starting on January 1, 2015. The last time the country sat on the council was 1993-94.
In addition to his letter to Key, Puna sent words of congratulations to Premier Toke Talagi on Niue’s 40th Anniversary of Self-Government.
This week, the island nation is celebrating the historic occasion, celebrating its achievement of independence in free association with New Zealand which occurred 40 years ago this month.
Similar sentiments were conveyed to Fiji Leader Frank Bainimarama on the occasion of Fiji’s independence anniversary on October 10, as well as the Prime Minister of Spain for its national day, said advisor Trevor Pitt with the Office of the Prime Minister.