A draft charter for the organisation, which will be chaired by Trump, has been sent to a number of world leaders - including Canada's Mark Carney, Türkiye's Recep Tayyip Erdogan and Argentina's Javier Milei.
It is unclear exactly how many countries have received invitations.
A spokesperson for the prime minister said he welcomed the beginning of the next phase of the peace plan for Gaza.
He was invited to join the board and will give it "due consideration".
Bloomberg revealed the text of the document said each country that accepted the invitation would be represented by its leader and would be given a term of "no more than three years".
If a country wanted to stay on, Bloomberg said, it would have to make a cash contribution to its efforts of $US1 billion ($NZ1.7 billion).
