The 78 year old was a former President of the Tonga Rugby Union and played an instrumental role in strengthening the union's governance and administrative structures.
World Rugby Chairman Sir Bill Beaumont said the global rugby community sends its deepest sympathies and condolences to the Pohiva family and the wider Tongan rugby community at this difficult time.
"As President of the Tongan Rugby Football Union, Mr Pohiva was a dedicated and proud supporter of the game of rugby. World Rugby will offer our full support to the ʻIkale Tahi, who are here in Japan preparing for Rugby World Cup 2019."
Last year Mr Pohiva reversed a decision by Tonga's Ministry of Education that appeared to ban girls from playing rugby in schools, saying his government "actively encourages the participation of every Tongan student in all sports without discrimination".
The 'Ikale Tahi squad are preparing for their opening match of the Rugby World Cup in Japan and learnt the news yesterday morning following a team meeting.
"On behalf of the 'Ikale Tahi Rugby World Cup squad I would to expresses our deepest sympathies to the Pohiva family with the passing of our Prime Minister, the Honourable Akilisi Pohiva, " said coach Toutai Kefu.
"Mr Pohiva was a proud, passionate Tongan who worked incredibly hard for his people. Mr Pohiva was a great supporter of Tongan rugby and provided strong support for 'Ikale Tahi. The 'Ikale Tahi will keep him in our thoughts and prayers."
Assistant coach Pita Alatini said Mr Pohiva will remain in their thoughts throughout the World Cup.
"It's definitely sad news and the boys have rallied around and just making sure that we pay the respects its due and that will carry through us I imagine all the way through until tournament and making sure he's in our thoughts going forward and making sure we pay our respects back in terms of our performances throughout the tournament."
World Rugby is currently liaising with the Tongan Rugby Football Union on an appropriate way to recognise Samuela 'Akilisi Pohiva's contributions to rugby.