In the meeting, Abe described Japan as an age-old friend of Iran, stressing that Tokyo will keep up efforts to reduce tensions in the Middle East.
For his part, Rouhani praised Japan for its efforts to save and implement the 2015 nuclear deal, known as the JCPOA.
He also stressed the need for the expansion of relations between Iran and Japan in various fields.
Rouhani has met several world leaders on the sidelines of the UN gathering.