The state said that terms of reference of the study and details of the agencies for conducting the tests should be shared to the party states and approved by the supervisory committee.
Mullaperiyar dam was built in 1895 on the Periyar river in Idukki district of Kerala.
Though Tamil Nadu had earlier agreed for the meeting, it has not yet responded even after two months.
When the water level is at 142 feet, the quantity of leak through the galleries is 185 litres of water per minute.
Tamil Nadu accepts the fact that the baby dam has weakened. This is the reason why it is constantly putting pressure on Kerala to allow measures to strengthen the baby dam.
Alleging that the Left government was constantly "cheating" people of Kerala over the dam issue, the Congress wanted Chief Minister Pinarayi Vijayan to break his silence over the matter.
Though the apex court had earlier assured to consider in detail issues regarding dam safety and maintenance, a detailed argument on the matter is unlikely today.
The decision to seek compensation was taken after Kerala Water Resources Minister Roshy Augustine's meeting with Chief Minister Pinarayi Vijayan.
Kerala sought the court's instruction to assign a joint committee comprising the representatives of both the states to decide on the time and quantity of water that has to be released.
About 7,141 cusecs of water is currently being drained off the dam located in Idukki district of Kerala.