The Government said it will, instead, look for alternative routes to implement the Sethusamudram Canal Project - a shipping channel between India and Lanka.
The ministry's affidavit asked the court to dispose of Swamy's petition in the wake of its fresh submission.
The former UPA government had in two affidavits filed in February and September 2013 told the apex court that it meant to pursue the implementation of the project given its advantages.
For this, a channel, passing through the limestone shoals of Adam's Bridge (which is also known as Rama's Bridge, Ram Setu, and Ramar Palam), was to be dredged in the Sethusamudram sea between Tamil Nadu and Sri Lanka.
Under the Sethusamudram project, a 83-km-long deep water channel would have been created linking Mannar with Palk Strait by extensive dredging and removal of the limestone shoals which constitute the Sethu.
Appearing on behalf of the Centre, Additional Solicitor General Pinky Anand said, "the Centre has filed the response in pursuance of the earlier directions and the PIL can now be disposed of".
In 2007, Swamy filed a petition challenging the then alignment of the project that would damage Ram Setu, following which the court stayed the project on August 31, 2007. The Rama Setu, Rama's Bridge or Adam's Bridge, the Sangh Parivar believes, was built by Lord Rama to cross over to Lanka to save Sita from the clutches of Ravana. The project required dredging in the region. In 2007, the Archaeological Survey of India (ASI) filed an affidavit before the top court asserting that Lord Ram was a mythical character and that the Ramayana had no historical basis, thereby implying that claims that the Ram Setu was built on instructions of the Hindu God were unsubstantiated and had no basis in history.
The Sethusamudram Shipping Channel project has been facing protests from some political parties, environmentalists and certain Hindu religious groups.
He had voiced apprehensions that the report may never be submitted in the Supreme Court as the consequences may be to the scrap the project itself. This was conveyed to the court in an affidavit filed by the Shipping Ministry.