During the meeting, Gogoi asked the centre to give its sanction on the proposal submitted by the Assam government for undertaking work on updating the National Register of Citizens, official sources said here.
The Chief Minister requested Shinde to strengthen the legal process for detection and deportation of illegal immigrants from the state, they added.
Gogoi, who is currently on a visit to the national capital, also held a meeting with Union Rural development Minister Jairam Ramesh.
The topic of discussion between them was regarding implementation of Pradhan Mantri Gram Sadak Yojna.
Ramesh assured Gogoi of sanctioning projects to connect by road all villages in Assam having a minimum population of 500 people during 2012-13 and 2013-14.