Reuters reports that the two men held closed-door talks to discuss a range of issues including multilateralism and the reinforcing of dialogue between diverse cultures.
They discussed "re-establishing faith in multilateralism, reinforcing dialogue among cultures and touched on international situations that merit particular attention", the Vatican said in a statement.
A visit by Benedict to the UN would be his first to the world body and his first trip to the US as pontiff.
Two previous popes have made official visits to the UN - Pope Paul VI and Pope Benedict's immediate predecessor John Paul II.
Church sources have speculated that the trip by Benedict, who was elected pontiff two years ago, could take place later this year during the UN General Assembly.
In a statement, the Vatican recalled the Church's contribution to the action of the United Nations in resolving current conflicts and reaching understanding between nations, a Zenit report adds.
UN chief meets Pope for the first time (ABC Radio Australia, 19/4/07)
UN Secretary-General invites Pope to visit (Javno, 18/4/07)
Secretary-General Invited Benedict XVI to the U.N. (Zenit, 18/4/07)
LINKS (not necessarily endorsed by Church Resources)
Ban Ki-moon (Wikipedia)
Ban Ki-moon (Official website)
United Nations (Wikipedia)
United Nations (Official website)
Mission of the Holy See to the United Nations
Stop Darfur violence, Holy See tells UN (CathNews, 14/12/06)
Holy See refuses to sign treaty over right to life concerns (CathNews, 15/12/06)
20 Apr 2007