He is expected to make a stop-over in Kabul on his way back home from Moscow where he is going for a two-day visit from Wednesday to hold annual summit with Russian President Vladimir Putin.
The Kabul visit has not been officially announced but informed sources said the Prime Minister will make his first trip to the war-torn country on Friday.
The Parliament building project, which was initially conceived at a cost of USD 45 million, was started by India in 2007 as a mark of friendship and cooperation to help rebuild Afghanistan.
Situated between historic landmarks King's Palace "Darulaman" and the Queen's Palace - the building has elements of Mughal and modern architecture and has Asia's largest dome as its key feature.
The building will house the Wolesi Jirga (Lower House) with a seating capacity of 294, a 190-seat Meshrano Jirga (Upper House), besides other facilities like conference hall and press room.
India has invested around USD two billion in aid and reconstruction and trained scores of Afghan officers.