The UN chief and the Lankan premier held close-door talks soon after Ban arrived in Colombo, officials said.
"The two men were likley to focus on peace, reconciliation and reconstruction," they said but did not give the details.
Earlier today, Ban was received at the Bandaranaike International Airport here by Deputy Foreign Minister Harsha de Silva.
The UN chief, who is on a three-day visit, would call on President Maithripala Sirisena tomorrow and visit the Sinhala-majority southern city of Galle.
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He is scheduled to speak at an event in Colombo on September 2 on 'Sustaining Peace - Achieving Sustainable Development Goals'.
This is Moon's second visit to Sri Lanka in seven years.
He visited the country days after the Sri Lankan troops defeated the Liberation Tigers of Tamil Eelam and ended the nearly 30-year separatist campaign in May 2009.
Since that visit, Lanka came under close UN scrutiny for its warcrimes accountability during the war with the LTTE.
The UN has been pushing for a special court to investigate the allegations.
Sri Lanka dismissed the figure as "excessive" but the UN human rights council passed three consecutive resolutions since 2012 demanding accountability for warcrimes blamed on both the government troops and the LTTE.