During their meeting, Modi expressed concern over Nepal's constitution drafting process, and in response, Koirala assured him that the new constitution would be ready within a year, The Himalayan Times reported.
Koirala attended Modi's swearing-in ceremony Monday and the two leaders held talks Tuesday. Koirala returned to Kathmandu Wednesday.
Koirala extended an invitation to Modi for the upcoming SAARC summit in November and requested him to visit Kathmandu even before the summit.
Modi accepted the invitation and said he was keen on visiting the Pashupatinath temple.
Koirala thanked India for its support to Nepal's peace building and constitution drafting effort and said he expected continued Indian support on these fronts in the future too.
Koirala at the meeting praised Modi for running an impressive election campaign that gave his Bharatiya Janata Party (BJP) an absolute majority in the Lok Sabha.
The two leaders discussed various bilateral issues, including harnessing Nepal's hydropower, development of tourism, road projects and fast tracking Tarai-Kathmandu road project for mutual benefit.