A bench headed by Chief Justice S.A. Bobde and comprising Justices S.A. Nazeer and Sanjiv Khanna noted Swamy's contention that his interim application be listed for urgent hearing on directions to Archaeological Survey of India to declare Ram Sethu as an ancient national monument.
"You please mention this after three months. We will entertain it," said the court.
In March 2017, Swamy had won the first round with the Centre assuring the apex court that it would not touch the Sethu, which is a chain of limestone shoals between coasts of India and Sri Lanka, for the construction of Sethusumundram Ship Channel project.
According to the epic Ramayana, the Ram Sethu bridge was built to rescue Sita, who was kidnapped by Ravana.
Swamy had insisted that although the Centre agreed to his demand, but nothing happened. The apex court cited pendency of several cases before it and asked the BJP leader to mention it after three months for urgent hearing.
The BJP leader had filed a PIL against the controversial Sethusamudram Ship Channel project, initiated by the UPA-I government. The apex court in 2007 stayed the work for the project on the Ram Sethu. The Centre had expressed willingness to explore another route to the project without damaging the Ram Sethu.
The project includes 83 km-long deep water channel to link Mannar with the Palk Strait, by extensive dredging and removal of limestone shoals.
The top court last year had granted six weeks to the Centre to put forth its stand on Ram Sethu, and also granted liberty to Swamy to move court.
( With inputs from IANS )