Both the states, which are members of the Pacific Small Island Developing States, are among the lowest-lying nations and face the greatest threat from the ill effects of climate change.
Speaking at the opening of the annual U.N. General Assembly session, Marshall Islands President Christopher Loeak urged an end to the endless North-South division and finger pointing, U.N. News reported.
Citing his country's national energy plan to cut emissions, boost efficiency and pursue new technology, Loeak said: "I ask of the world if you will also meet us in ambition. Will it come soon enough?"
He said his country is heavily dependent on international assistance and doesn't have other means needed to mitigate the effects of rising oceans.
Sprent Dabwido, president of the Micronesian republic of Nauru, said greenhouse gas emissions continue to rise each year with no end in sight.
"Small islands may be the canary in the coalmine, but we are all staring a global catastrophe right in the face," he warned.
"If multilateralism is to have any credibility, then we must move to an emergency footing and those countries with the greatest capacity must immediately begin mobilizing the significant resources necessary to remake the energy infrastructure that powers the global economy," he added.