"We are here all to help you. I hope you will not betray and disappoint us. I sincerely count on your leadership," Ban said shortly after Salva Kiir addressed the high-level meeting at the United Nations by video link.
The peace deal, aimed at ending 21 months of civil war between Kiir's government and rebels, has been marred by heavy fighting.
The army and armed opposition repeatedly accuse each other of breaking an internationally brokered August 29 ceasefire deal, the eighth such agreement to have been signed since civil war broke out in December 2013.
But he also promised what the international community, deeply frustrated that the world's newest country degenerated into devastating civil war just two years after independence, wanted to hear.
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"I am deeply committed to the full and timely implementation of the agreement and I have the moral and constitutional responsibility to restore peace and development for my people," Kiir said.
"I am determined to stop this senseless war and make sure, together with my brothers in the armed opposition... (to) build a democratic, united and harmonious country by implementing the agreement," he added.
The violence has killed tens of thousands of people and split the impoverished country along ethnic lines.
Ban welcomed Kiir's "strong commitment" to the agreement in his address to the meeting on the sidelines of the UN General Assembly.
"We are all with you Mr President," Ban told Kiir. "I wish you all the best," he added to applause.
UN aid chief Stephen O'Brien said South Sudan's humanitarian needs would continue for "some years" even if the fighting stopped today, costing the international community USD 1 billion a year.