Tamil Nadu Chief Minister J Jayalalithaa and her Karnataka counterpart Jagadish Shettar will meet in Bangalore on Thursday in an effort to find a solution to the Cauvery water sharing row.

The meeting comes after the Supreme Court yesterday asked both the Chief Ministers to meet and arrive at an amicable solution to the "sensitive" water dispute.

A Tamil Nadu government release said the Chief Minister would meet Shettar on November 29 and discuss the issue keeping the farmers interests in both the states as suggested by the apex court.

"Why the two Chief Ministers can't sit together? Give it a try, it is not impossible," a bench of justices D K Jain and Madan B Lokur said yesterday.

"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 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 "the Chief Ministers should not meet just for coffee but they should meet along with their experts to find a solution".

The court urged both the Chief Ministers to have a meeting and posted the matter for directions on Friday.