The invitation was extended on the eve of New Year when General Bajwa reached the Afghan leaders on telephone.
Army spokesman Major General Asif Ghafoor said in a tweet that General Bajwa called Afghan President Ashraf Ghani and Chief Executive Abdullah Abdullah and "conveyed best wishes for 2017 and pledged to work together for peace in the region".
He also said that "peace in both countries is in greater interest of the region".
It was not known when Genera Bajwa will pay the visit which would be his first since taking over charge of the Pakistan Army in November.
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