The meeting took place amid heavy security at the presidential palace, which still bears the scars of the past 30 years of conflict in the central Asian state.
Earlier this month, UN Special Representative to Afghanistan, Tom Koenigs, said Mr Ban would make the establishment of the rule of law in Afghanistan a top priority at a conference to be held in Rome on July 2 and 3.
Mr Ban also met General Dan McNeill, the US commander of NATO forces in Afghanistan, with Afghan anger boiling over the growing number of civilian casualties resulting from US and NATO military operations against insurgents in the south and east of the country.
The soldiers arrested 15 people during the pre-dawn raid in Khogiani district, on the outskirts of the provincial capital of Jalalabad, Lal Gul, the head of Afghanistan's Human Rights Group said.
A US military official confirmed the operation and said coalition soldiers killed three militants after they came under fire and arrested 16 more militants.
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