The leaders said they saw minimal, if any impact, by departing the region's primary body.
Fiji's Prime Minister Frank Bainimarama says Micronesia must stand in solidarity with their Pacific counterparts.
The standoff stemmed from Micronesia's frustration at its candidate no getting the sceretary-general's position at the Forum Secretariat following what it called a 'gentlemen's agreement' the subregion would get the top job at PIFS.
Former Cook Islands prime minister Henry Puna was elected to replace Papua New Guinea's Dame Meg Taylor last month.
Bainimarama, who takes up the forum chair position when the leaders meet in August, said like any other family, the forum had its disagreements but "we are held fast together by thousands of years of shared culture, traditions and history, and now by shared political, strategic and economic interests.
As sovereign nations with common challenges and a common destiny, we can be proud of what we have achieved together, he said.
"With climate action finally at the top of the agenda for the United States, we have a window of opportunity to enlist a global superpower in the pursuit of a resilient net-zero future we've all fought so hard to make reality.
"I have invited President Joe Biden to the Pacific Forum Leaders meeting this August to join our nations on the frontlines of the climate emergency.
"It would be among the most powerful acts of solidarity the new American President could show the climate-vulnerable."
The Fijian leader said it was an opportunity that deserved every measure of the forum's collective support.