The Iranian president and the UN chief held talks on the sidelines of the 70th session of the UN General Assembly.
Rouhani is also scheduled to meet with his French counterpart Francois Hollande on Sunday.
On Friday, he also sat down with Brazilian President Dilma Rousseff and Swedish Prime Minister Stefan Lofven at the UN headquarters.
President Rouhani, at the head of a high ranking delegation, is attending the 70th session of the UN General Assembly underway at the UN Headquarters.
Top diplomats attending the session discuss a broad range of crucial issues, including human rights, disarmament, nuclear safety and global terrorism.