Citing the UN Charter, Waqa said the 23 million people in Taiwan should have the same fundamental rights as others, regardless of the country's size.
He said Taiwan has contributed to the World Health Organisation and the International Civil Aviation Organisation (ICAO), and has supported the UN's goal of sustainable development.
Taiwan also took the lead in the development of low-carbon economy, Waqa said.
Taiwan is a key stakeholder in the international community, and its bid to participate in the United Nations-affiliated organizations should be supported, he said.
Nauru was the first of Taiwan's 22 diplomatic allies to express support for its international efforts, at the UN meeting at which 38 national leaders spoke on Wednesday.
The leaders of two other Taiwan allies -- Dominican Republic President Danilo Medina Sanchez and Honduran President Juan Orlando Hernandez Alvarado – addressed the UN General Assembly that day but did not mention Taiwan's bid to participate in the ICAO.
President Juan Carlos Varela Rodriguez of Panama, another of Taiwan's allies, also spoke on Tuesday but did not address the Taiwan issue.
Over the past two years, 16 of Taiwan's diplomatic allies, mostly Caribbean and Asia-Pacific countries, have expressed support for Taiwan at the UN General Assembly