"We have received the letter from National Conference claiming support of 16 members in the LAHDC Kargil," Deputy Commissioner Kargil Fida Hussain, who is also the election authority, told PTI.
He said the NC claim will be tested on the floor of the house when the first meeting of the newly-elected members takes place.
"We have not fixed the date for the meeting yet," he added.
While 26 members are elected, four members are nominated by the government.
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While Congress secured 10 seats, National Conference bagged eight seats and the remaining eight went to independents.
After the results were declared on August 28, five independents threw their lot behind the Congress while three supported the National Conference.
However, Chief Minister Omar Abdullah nominated four members from his party to the Council, upsetting the local Congress leaders.
Congress has decided to convene a meeting of Coalition Coordination Committee tomorrow to discuss the issue with the National Conference leadership in a effort to end the stalemate.