The parties urged the Tamil Nadu government to take steps to prevent Karnataka from going ahead with its move.
"The newly-formed AIADMK government should immediately take up the issue with the Centre and prevent Karnataka's proposed move," DMK working president M K Stalin said in a statement.
Terming Karnataka's decision as "unilateral", he said DMK was of the opinion that the move would harm "relations between the two states".
CPI(M) Tamil Nadu unit secretary G Ramakrishnan while condemning the neighbouring state for taking steps to go ahead with its plan, demanded that the Centre immediately intervene and prevent construction of the new dam.
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CPI state secretary V Durai Manickam echoed similar views.
"The Chief Minister should convene a meeting comprising various political parties, farmers associations and press the Centre on the issue," he said.
Karnataka had proposed to construct check dams across the Cauvery at Mekedatu.
The state claims that the project would meet the drinking water needs of Bengaluru and other towns that would arise in future in the Cauvery basin in Karnataka.