Sharif met Ban before his speech to the UN Sustainable Development Goals here today.
According to the Pakistan mission, Sharif urged the Secretary-General to play a role in defusing tensions between Pakistan and India and to help end alleged violations at the Line of Control.
Sharif called for implementation of United Nations Security Council resolutions on the Kashmir dispute and holding of plebiscite to determine the wishes of the Kashmiri people.
The meeting is understood to have been dominated by the Kashmir issue.
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India has maintained that the Kashmir issue is a bilateral one and the UN has no role in it.
The Pakistan Premier is currently in New York to attend the 70th United Nations General Assembly session, where his address is scheduled for September 30.
The Pakistan mission here said the UN chief voiced concern over the tensions between India and Pakistan and said his good office were available.
On Afghanistan, Sharif said Pakistan seeks to build a new relationship with its neighbour and expressed his country's readiness to assist in promoting the Afghan reconciliation process if asked to do so.