The delegation wanted a settlement bypassing a tribunal, before which the dispute is pending, but got no concrete assurance from the Prime Minister, according to Siddaramaiah.
He said the delegation explained to Modi the situation in Karnataka regarding protests over Mahadayi river water issue.
"The Prime Minister has not given any specific promise. But, still we hope that he would convene the meeting of the Chief Ministers of concerned states and he will try to resolve the issue," he told reporters.
The meeting comes against the backdrop of agitation being witnessed in several parts in north Karnataka including Hubli and Dharwad over the dispute.
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Siddaramaiah recalled an instance in the past when the then Prime Minister Indira Gandhi persuaded the Chief Ministers of Karnataka, Andhra Pradesh and Maharasthra to spare five TMC of water each from allocated share in Krishna waters for the benefit of Tamil Nadu for meeting its drinking water supply to Chennai.
"There is no problem as far as Mekedatu is concerned. We will go ahead with Mekadatu dam construction," the Karnataka Chief Minister said.
Karnataka government also requested the Prime Minister to allocate over Rs. 3,000 crore under the State Disaster Response Fund (SDRF), in the light 126 Taluks in the state having been declared as drought affected.
In a memorandum submitted to Modi, the Chief Minister has also sought Centre to release Rs. 3050.72 crores under SDRF and an additional 1500 MW of power be allocated from the Central Generating Stations to Karnataka.
Responding to this, the Prime Minister said a central team is being sent to the state, at the earliest, to assess the situation, the statement said.