In June 2020 Puna announced his intention to stand down as prime minister in September to compete for the role of secretary-general of the Pacific Islands Forum.

[12] The petition was upheld, with several voters being disqualified; the subsequent recount produced a tie,[13] precipitating the 2005 Manihiki by-election which Puna ultimately won.

[23] Shortly after being elected, Puna faced international condemnation after suggesting that the Cook Islands' first HIV victim should be quarantined or deported to prevent the disease from spreading.

[24] In February 2011 he shifted the focus of state-owned enterprises from making profits to providing improved services,[25] and announced greater transparency over the travel costs of Ministers and MPs.

[31] In September 2011 he announced that his government would establish a one million square kilometer marine protected area in the southern Cook Islands.

[38][39] While Forum Chair, he called for the restoration of democracy in Fiji following the 2006 Fijian coup d'état[40] and for stronger action on climate change.

[42] In August 2013 Marine Resources Minister Teina Bishop was stood down from Cabinet following allegations of corruption and fraud in his handling of his portfolio.

[46] In April 2014 Puna made a controversial decision to dissolve Parliament early for elections, leading to the resignation of Teina Bishop from Cabinet and his departure from the Cook Islands Party.

[47][48] Puna's government eked out a narrow victory in the 2014 Cook Islands general election, winning 13 of 24 seats on a minority of the votes, but lost its majority after electoral petitions.

[57] The plan was immediately ruled out by New Zealand Prime Minister John Key, who saw it as necessarily requiring independence and an end to shared citizenship.

[61] In December 2015 he attended the 2015 United Nations Climate Change Conference in Paris, France, where he joined other Pacific leaders in accusing the world of dragging its feet.

[68] A month later Puna announced that the Marae Moana marine park, planned since 2011, would cover the country's entire exclusive economic zone.

[76] In December 2019, a private prosecution for fraud was lodged against Puna and Deputy Prime Minister Mark Brown, alleging that a government-chartered aircraft had been misused.

[79] On 29 March 2020, while New Zealand was in lockdown, he announced plans for a quarantine station in Auckland to allow Cook islanders in the country to return home.

[82][83] In early June, Puna announced plans to re-open borders to Cook Islanders and work permit holders who had been living in New Zealand,[84] and expressed hopes for a tourism "bubble".

[86] On 17 June 2020 Puna announced his intention to stand down as Prime Minister in September to compete for the role of Secretary-General of the Pacific Islands Forum.

[7] In response to his election, Palau announced that it would be leaving the Pacific Islands Forum, claiming that a "gentlemen's agreement" to rotate the position between Polynesia, Melanesia, and Micronesia had been violated.

[97] Four members of the Micronesian bloc – the Marshall Islands, Kiribati, Nauru, and the Federated States of Micronesia – decided to hold a virtual meeting to discuss whether to exit the Forum.