The visit comes ahead of Sharif's upcoming visit to the US later this month. It will be the first after elections took place in Afghanistan.
"During his day-long visit, army chief General Raheel Sharif would meet Afghan President Ashraf Ghani, CEO Abdullah Abdullah, Defence Minister, National Security Adviser and senior military leaders," military spokesman Major General Asim Bajwa tweeted.
A defence official said Pakistan is perturbed by cross-border attacks by fugitive Taliban militants hiding in Kunar and Nuristan provinces of Afghanistan.
Pakistan also complains that Kabul failed to provide help during military's operation in insurgency-hit North Waziristan when it took no action against militants who fled across the porous border.
"Pakistan wants Afghanistan to act against the militant operation (being carried out) from its soil," he said.
Other issue of border management, intelligence sharing and Afghan concerns about Afghan Taliban will also be discussed.
Army has said more than 1,100 terrorists have been killed during operation Zarb-i-Azb launched against Taliban in North Waziristan in mid-June, while around 50 were killed in Khyber-I offensive against militants in the Khyber tribal district.
According to officials, the operation will continue till the extremists are completely wiped out.
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