Mr Kuhad will be the third advocate to represent the government in the case.
Solicitor General Mohan Parasaran recused himself earlier because his father, former Attorney General of India K Parasaran, appeared in the case wanting the project scrapped.
Senior Advocate Rajeev Dhavan had then appeared for Centre. However, the Supreme Court was told today that Advocate Dhavan has been replaced by Mr Kuhad, and the Centre will need three weeks for him to study the case.
Sources have told NDTV that Advocate Dhavan didn't receive necessary papers for the case despite his repeated requests to the government, due to which he recused from the case.
The Supreme Court is hearing petitions from Subramanian Swamy, Tamil Nadu Chief Minister J Jayalalithaa and Hindu religious organisations on scrapping the Sethusamudram project. The project links India with Sri Lanka, cutting short the travel time by sea.
However, it also cuts across the Ram Setu, a mythological bridge revered by the Hindus. The Supreme Court had restrained the Centre from cutting across Ram Setu and ordered for an alternate route. An expert panel opined that the project is not viable financially and ecologically. But Centre rejected the panel's recommendation.
The Supreme Court will take up the case after three weeks.