Ban recalled having personally pressed Mugabe in "very tense" private talks two weeks ago in Doha to accept the power-sharing agreement reached on September 15 with opposition leader Morgan Tsvangirai.
Ban, asked whether he backed calls for Mugabe to leave office, told a Geneva news conference: "I have urged him as hard as I could to honour his commitment as a political leader and as president of Zimbabwe to leave his legacy in a positive way."
Western leaders and some within Africa have called on Mugabe to step down amid a political crisis compounded by an economic meltdown and cholera epidemic.
Mugabe said on Thursday the water-borne outbreak, which has now infected 16,700 people and killed 792 of them since August, was under control.
But Ban said that reports he had received from the World Health Organisation and other U.N. aid agencies were "alarming".
"Therefore, I cannot agree that the cholera epidemic was over. We will continue to monitor and try to help those people."