A bench comprising Justices Ranjan Gogoi and Navin Sinha asked both the states to file the lists within two weeks in the original lawsuit preferred by Tamil Nadu against its neighbour in 2012.
Umapathy, the counsel for Tamil Nadu, said that the state would file the list within the stipulated time.
Earlier, the apex court had framed issues, including the question whether the Neyyar can be classified as inter-state river in the matter.
One of the issues was whether the stoppage of water by Kerala to Tamil Nadu in 2004 was an unlawful variation of the Neyyar Irrigation Project protected under the 1956 Act.
The other major issue to be considered by the apex court would be whether domestic supply of water in Kerala has a first charge over the claims of Tamil Nadu for water under the Neyyar Irrigation project.