"He leaves us sad & devastated. RIP Lance Naik Hanamanthappa. The soldier in you remains immortal. Proud that martyrs like you served India," Modi tweeted.
The soldier died today, four days after he was miraculously rescued alive from beneath tonnes of ice at a height of 19,600 feet after the February 3 avalanche hit.
Koppad was among 10 soldiers in the high-altitude military post which was struck by the avalanche and nine of them, including a Junior Commissioned Officer, had died earlier.
"Demise of soldiers in Siachen is very tragic. I salute the brave soldiers who gave their lives to the nation. Condolences to their families," Modi had tweeted on February 4, a day after the avalanche struck.
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Defence Minister Manohar Parrikar had also condoled the death of the soldiers.
"My heartfelt condolences to the near and dear ones of our brave soldiers who were martyred in the line of duty in the most difficult terrain of Siachen," he had said on that day.
The 33-year-old soldier of the 19th Battalion of Madras Regiment is survived by his wife Mahadevi Ashok Bilebal and two-year-old daughter Netra Koppad.
A resident of village Betadur in Dharwad district of Karnataka, Koppad had joined the army 13 years back.
The condition of Koppad, who was admitted to Army Research and Referral Hospital here on February 9, had deteriorated yesterday.