The summit marks the 100th anniversary of Mandela's birth.
The Taoiseach and the Tánaiste are headed stateside this week to attend high-level meetings and United Nations events in New York.
Varadkar will attend the Nelson Mandela Peace Summit on Monday, in which Ireland played a prominent role, having led the negotiations in partnership with South Africa which agreed to the political declaration issuing from the summit.
The summit – which aims to celebrate the legacy of Nelson Mandela and seeks to renew the determination and responsibility of UN member states to apply his values – will see the Taoiseach deliver a statement in the UN General Assembly Hall.
“I’m looking forward to returning to the United Nations this week to participate in the Nelson Mandela peace summit," the Taoiseach said in advance of the trip.
"This event marks an important opportunity to reflect on Mandela’s legacy. It’s not only a celebration of his life, but also a moment for the global community to see how Mandela’s commitment to peace, reconciliation and human rights, can help us to meet the challenges we face today.”
The Minister of State for the Diaspora and International Development, Ciarán Cannon, will also attend, along with representatives of 193 member states who are gathering for the annual United Nations General Assembly.
The Taoiseach, Tánaiste and Minister of State, while in New York, will also hold bilateral meetings with counterparts from around the world.
Ireland’s campaign for election to the UN Security Council for the 2021-2022 term was formally launched in July, and this week is an opportunity for Ireland’s candidature to be raised with member States whose backing is essential at the election in June 2020.
The Taoiseach and Tánaiste will highlight Ireland’s long-standing commitment to the UN, including Irish participation in UN peacekeeping operations.
During his visit, the Tánaiste will speak to the United Nations General Assembly, emphasising the importance of multilateralism in meeting the many challenges facing the world today.
“Our world today is imperilled by challenges which no country alone can solve," Coveney said ahead of the meeting.
"Ireland is determined to play a role and meet our responsibilities at the United Nations. From protecting our planet to providing humanitarian assistance to the most vulnerable, we must work together in partnership and with understanding.
"The UN General Assembly provides Ireland with a unique opportunity to project our values as a nation, and also to gain insights from others. While in New York I look forward to meeting with many leaders to discuss how we can work together to build peace and stem the tide of conflict globally."
Other programme elements will include the Tánaiste attending the signing ceremony for the
Treaty on the Prohibition of Nuclear Weapons (TPNW).
The TPNW includes a comprehensive set of prohibitions on participating in any nuclear weapon activities.
Ireland, as one of the Core Group which put forward the UN Resolution which led to the adoption of the Treaty last year, was among the first States to sign it in 2017.
