The permanent representative of Nigeria told reporters after his unanimous election by the Assembly, "We will try to hasten those negotiations in the spirit of fairness" and also with the sense that 75 years after its founding the UN cannot continue to "speak the language" it did 50 or 70 years ago.
The Intergovernmental Negotiation (IGN) process for Council reforms "has not moved as fast as we have wanted to" he said. "But certain things are clear: No delegation thinks it is fair to continue without a reform of the Security Council".
India is heavily invested in the reform of the Council as it aspires for a permanent seat.
Africa, which makes up the largest group in the UN and where most Council-mandated peacekeeping operations are taking place, also urgently wants the reform so it can be represented among the ranks of the permanent members.
Muhammad-Bande said, "For the (African) continent there is a consensus, but reform of the Security Council is not only for one group. It is a consensus element involving member states. We will continue to push this."
The current situation is "untenable" and it is import for "the delegations that are further apart to see whether we can continue to narrow the differences", he said.
"We have to continue not to lose sight of the goal which is to have fair, just and quick reform," he added.
Muhammad-Bande, who was backed by the African Union, will take over from Ecuador's Maria Fernanda Espinosa when the 74th session of the Assembly begins in September.
Congratulating him, India's Permanent Representative Syed Akbaruddin tweeted: "A friend of India is elected as next Prez of @UN General Assembly."
Speaking at the Assembly soon after his election, Muhammad-Bande said that he will prioritise the elimination of poverty, zero hunger, quality education, and climate action.
"I am committed to promoting partnerships that are needed from all stakeholders to achieve our objectives, and ultimately ensure that we do our best to ensure peace and prosperity, particularly, for the most vulnerable" he said.
Under his presidency, the Assembly will prepare for the 75th anniversary of the founding of the UN next when it is expected to unveil landmark initiatives.
He listed several important Assembly meetings scheduled during his presidency, including the high-level political forum and the Secretary-General's Climate Summit in September, the high-level events on Universal Health Coverage, and Beijng+25, which will review the progress of women's status since the landmark conference in 1995.
These, he said, "provide major opportunities to promote the implementation of our goals and targets, and we must seize each of those opportunities to galvanise political momentum and action at the highest level".
The post of the Assembly President rotates among geographic regions and it is Africa's turn for the next session.
An academic before becoming Nigeria's UN envoy, he had served as the Vice-Chancellor of the Usman Danfodiyo University in Sokoto and the Director General of the National Institute of Policy and Strategic Studies in Kuru.
(Arul Louis can be reached at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )