Buhari stated this on Tuesday night while delivering Nigeria's National Statement via video link on the first day of the 75th session of the Uníted Nations General Assembly (UNGA) Debate.
The President pledged Nigeria's commitment to working with member states in the spirit of global cooperation and solidarity to promote human health and general well-being.
The theme of this year's General Assembly is "The Future We Want, The United Nations We Need: Reaffirming Our Collective Commitment to Multilateralism- Confronting Coronavirus Through Effective Multilateral Action."
The Nigerian leader described the theme of the conference as most appropriate and timely, saying that it captured the common desire for a renewed and revitalised UN in need of multilateral approaches to the many challenges facing the world.
"As we reflect on the future we want and the United Nations we need, we must realise that the people of the world not only look up to us: they count on us.
"If the United Nations system cannot mobilise the world to marshal out a truly effective and inclusive response to the coronavirus pandemic, then the United Nations would have failed in the core mission of giving expression, direction, and solution to the yearnings of the international community.
"The future we want must guarantee human rights, human dignity, human prospects and prosperity.
"The principles of 'Leaving No One Behind and Doing No Harm' must be expressed through accountability, strategic growth initiatives, and elimination of threats of all kinds," he said.
He said that in order to give hope for a bright future and prosperity for all Nigerians, his administration had embarked on measures aimed at ensuring national resilience.
"We intend to achieve this through the implementation of the Economic Sustainability Plan and the Medium Term National Development for the periods 2020-2025, and 2026-2030.
"We expect that these ambitious initiatives will deliver sustainable economic growth and development to Nigeria," he said.
Speaking on the coronavirus pandemic, Buhari stressed the need for effective multilateral actions aimed at tackling the situation.
He expressed concern that the pandemic had devastated the world economy and strained the capabilities of health systems of many countries, including Nigeria.
"In the aftermath of the coronavirus outbreak in Nigeria, we prioritised vulnerable groups, including women, children, older persons, and the unemployed, in our efforts to provide medical and social assistance to cushion the socio-economic effects of the disease.
"Accordingly, we have expanded our National Social Register to include an additional one million Nigerians.
"Our National Social Investment Programme (NSIP) has been the vehicle for reaching out to the poor and vulnerable members of the Nigerian population, as well as providing cover for over 12 million households," he said.
While applauding the UN and WHO for the efforts they put in to help combat the pandemic, Buhari noted with appreciation the two billion dollars Global Response Plan launched by the UN Secretary-General to fund the coronavirus response in the poorest countries.
He also applauded the Secretary-General's call for a cease-fire in conflict areas so that humanitarian assistance could reach groups vulnerable to the virus.
On poverty eradication in Nigeria, the president said that in order to mitigate its impact, his administration had embarked upon the disbursement of N10.9 billion to households engaged in Micro, Small, and Medium Enterprises as palliatives.
According to him, an additional N500 billion fiscal stimulus package as well as sustained delivery of humanitarian and social interventions to cater to poor and vulnerable households have been established.
He added that the Central Bank of Nigeria had also launched a N3.5-trillion-stimulus package to boost manufacturing and facilitate import substitution.
The Nigerian leader then urged the international community to complement efforts being made to address poverty, particularly in developing countries.
In this regard, he commended the outgone President of the 74th General Assembly, Prof. Tijjani Muhammad-Bande of Nigeria, for launching an Alliance for Poverty Eradication in June.
He enjoined global leaders, particularly from the global North, to support the alliance at a time when "the COVID-19 is reversing gains made toward the achievement of the 2030 Sustainable Development Goals (SDGs) and pushing an additional half a billion people into extreme poverty."
On disarmament, international peace and security, Buhari said "Nigeria remains deeply concerned over the illicit trade, transfer, and circulation of small arms and light weapons, particularly on the continent of Africa."
He, therefore, called on the international community to renew efforts that would help stem such activities and promote the Arms Trade Treaty in order to codify accountability in the battle against trans-border crimes, including terrorism and acts of piracy.
On terrorism and counter-terrorism, the president urged world leaders to redouble efforts at ensuring collective security, saying that the litany of sophisticated terrorist attacks across the globe "is a harsh reality of the challenges the world is facing today."
"In Nigeria, we are still facing violent extremism from the insurgency of Boko Haram and bandits.
"We continue to count on our strong cooperation with UN counter-terrorism bodies and neighbouring countries to overcome the terrorists in the Lake Chad Basin and the wider Sahel Region.
"We will vigorously sustain the rehabilitation, reconstruction, and resettlement of victims of terrorism and insurgency in the North East.
"The North-East Development Commission has been established for that purpose," he said.
On illicit financial flows, Buhari said that global aspiration to recover from the impact of COVID-19 would not be fully met without addressing structures making it more difficult for countries to generate and retain their financial resources.
In this regard, the president again thanked Muhammad-Bande as well as the immediate past President of the Economic and Social Council, Amb. Mona Jul, for jointly launching the High-Level Panel on International Financial Accountability, Transparency and Integrity (FACTI) for Achieving the 2030 Agenda.
Meanwhile, a statement by Mr Femi Adesina, the President's spokesman, indicates that Buhari also spoke on other issues that are of interest to Nigeria.
Adesina said that speaking on climate change, the Nigerian leader reiterated his country's commitment to revitalising Lake Chad.
"We are convinced that recharging the Lake will improve the living conditions of our people in the area, promote inter-state cooperation, strengthen community resilience, and assist in addressing environmental as well as security challenges threatening the region and its resources," he said.
Buhari, therefore, renewed his call for international support for the regional efforts being made to raise 50 billion dollars required to revitalise the lake.
On quality education, Buhari announced that Nigeria would be hosting the 4th International Conference on Safe Schools in 2021.
"Quality education for all is the cornerstone of sustainable development.
"I invite you all to Nigeria to participate in the conference, which aims to advocate the protection of education from attack as we work together towards the future we want," he said.
Buhari ended his speech at the virtual event by reaffirming Nigeria's commitment to promoting international peace and security and sustainable development.
He also said that Nigeria remained committed to strengthening partnerships and cooperation with international organisations.
The general debate is held at the beginning of each session of the UNGA, usually in September in accordance with the Rules of Procedure.
Often member states are represented by their Heads of State or Government during the general debate. Not all member states participate in every session.
The general debate provides an opportunity for member states to raise any topic and statements often reflect issues of importance to the member state.