Malcolm Turnbull is due to meet the American president on Thursday in New York.
Bainimarama, who is in Australia, said he has asked Turnbull to reinforce his earlier message to 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, Bainimarama said his message was simple.
He called on the US president not to “let the side down” by leaving the Paris Agreement when there was a “clear game plan” and so many “scores already on the 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.
Bainimarama said the response to Fiji’s appeal for funds for its presidency have been disappointing and he says he has appealed for more assistance.
He appealed for everyone to keep up the momentum over dealing with climate change.
“Where governments fail to lead, the private sector must do so – as is happening already in America.
“Where the call to action goes unheeded, civil society must mobilise ordinary people to turn up the pressure. And where politicians deny the magnitude of the challenge we face, men and women must use their power at the ballot box to replace them,” Bainimarama said.
Bainimarama also appealed to developed nations to follow through commitments over climate finance.
He said there were three critical areas where the private sector could help – more finance for adaptation, new investment for areas like renewable energy and access to water and more affordable access to insurance cover for climate-related events.