During the meeting at the Rashtrapati Bhawan, Ban described India as a "critically important global power" and said he was aware of its "aspirations" along with those of many other countries for reform of the UN and their desire to play a leadership role in the UN Security Council.
Mukherjee said the reforms in the UN are essential to enhance its "credibility" and "legitimacy" so that it represents the geo-political realities of today.
"Reforms of the United Nations should be advanced at least in the 70th year of the UN. India hopes and counts upon the UN Secretary General's leadership and persuasive skills to steer the discussions for urgent reform of the UN," the President said. The UN will turn 70 on October 24 this year.
India is an aspirant for permanent membership of the expanded Security Council.
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Mukherjee underlined that "The UN should play an effective role in all situations. A reformed and effective UN will be able to respond to the crises afflicting the world in a more decisive manner."
Ban appreciated India's contribution to the UN and said he always wanted to forge stronger ties with this country.
"The UN Security Council must become effective, representative, democratic and transparent," he said.