"Why can't the two Chief Ministers sit together? Give it a try, it is not impossible," a bench of justices D K Jain and Madan B Lokur said.
"We want you to meet in a congenial manner and discuss the issue in the larger interest of farmers from both states," it said.
The court said that it is not possible for Cauvery River Authority (CRA) headed by the Prime Minister to meet, so the state governments should meet to find a solution.
"Try to find out a solution through give and take," the bench said, adding that "the chief ministers should not meet just for coffee but they should meet along with their experts to file a solution".
Senior advocate Fali S Nariman, appearing for Karnataka, said there is no problem in meeting and the Karnataka Chief Minister will certainly meet.
Counsel appearing for Tamil Nadu, however, remained non-committal and said that he will have to take instructions from the concerned authority.
The bench urged both the Chief Ministers to have a meeting and posted the matter for directions on Friday.
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