Puna was in New Zealand last week to meet the New Zealand prime minister Jacinda Ardern.
He led a Cook Islands delegation which also included Finance minister Mark Brown, Office of the Prime Minister chief of staff Bredina Drollet and Foreign Affairs secretary Tepaeru Herman.
The delegation also met up with deputy prime minister Winston Peters. However, no details of the meeting have been released so far.
In the lead-up to the New Zealand meeting, Brown was in China attending the 2017 Guangdong International Tourism and Culture Festival.
He also opened the Cook Islands Photo Exhibition at the Guyuan Museum of Art in Zhuhai.