Malcolm Turnbull is due to meet the American president on Thursday in New York.
Mr Bainimarama, who is in Australia, said he has asked Mr Turnbull to reinforce his earlier message to Mr Trump for the US to stay in the Paris Agreement and to continue to take a leadership role.
In his speech in Melbourne at the opening of the 4th Australasian Emissions Reduction Summit Mr Bainimarama said his message was simple.
He called on the president not to let the side down by leaving the Paris Agreement when there was a clear game plan and so many scores on board.
He said Fiji's priority, as president of the COP23 climate change talks in Bonn in November, was to build a grand coalition of governments, civil society and the private sector to defend the agreement and come up with an action plan.
Mr Bainimarama said the response to Fiji's appeal for funds for its presidency had been disappointing and he said he had appealed for more assistance.
Photo: Fiji Government The prime ministers of Fiji and Australia - Frank Bainimarama and Malcolm Turnbull - at the Australian PM's Sydney residence