Officials said during the half-an-hour meeting, the two leaders discussed India-US bilateral relations, including the implementation of the civilian nuclear agreement between the two countries.
The meeting was considered significant in view of the fact that it came ahead of the India-US civilian nuclear cooperation bill that is expected to come up in the Senate for voting next week.
Besides bilateral relations, Mukherjee discussed regional and international issues of common interest and concern with Dr Rice.
The defence minister was accompanied by Foreign Secretary Shyam Saran, who had met with Under Secretary of State for Political Affairs Nicholas Burns and Counselor in the State Department, Philip Zelikow on Wednesday.
Mukherjee, who arrived in New York at the head of a 12-member delegation on September 19, is slated to address the General Assembky on September 27.
On Thursday, Mukherjee also met with Sheikha Haya Rashed Al-Khalifa, the president of the 61st UN General Assembly, who spoke of the need for all member countries of the UN to make efforts to revitalise the organisation, particularly as it has completed its 60th year.
Officials said areas of focus that emerged in the meeting included developmental issues and the counter-terrorism strategy, adopted in early September by the last General Assembly.
The defence minister also participated in an informal luncheon meeting of ministers of the South Asian Association for Regional Cooperation, hosted by Bangladesh Foreign Minister Morshed Khan in his capacity as the current chairman of SAARC.
Besides discussing ways of improving coordination between SAARC countries and the need for implementing the agenda set by the leaders of the SAARC nations at the summit in Dhaka in November 2005, the group considered ways of expanding coordination at all levels among the SAARC nations.
Officials said in his capacity as the representative of India, the incoming SAARC chair, Mukherjee gave the vote of thanks. He underlined the importance of expanding coordination among the SAARC nations to realise the potential of the group, its constituent countries and to realise the vision of the founding fathers of SAARC.