Kiribati President, Taneti Maamau, made the call while addressing the Assembly in New York.
He said the meeting's theme implied that the UN is one family, so Taiwan should be included in international processes and discussions.
"This theme will be irrelevant if the UN continues to ignore the 20 million people who live and contribute to our shared home and continue to exclude them from the process."
Nauru President, Baron Waqa, backed up sentiments and said making the United Nations relevant to all people, must include the people of Taiwan.
"The people of Taiwan should be treated equally to those of other nations."
Taiwan lost its seat on the UN in 1971.
Kiribati and Nauru are two of six Pacific nations, including Palau, the Marshall Islands, Solomon Islands and Tuvalu, who recognise Taipei over Beijing.
Photo UN Media. Caption: Nauru President Baron Waqa speaking at the UN General Assembly