"He continues to battle the odds and his medical condition remains very critical," a medical bulletin issued by Army Research and Referral Hospital here said.
Hanamanthappa remains ventilator-dependent since arrival in the hospital yesterday, it said.
The medical team at R&R Hospital is monitoring his situation continuously and is treating him with best expertise and resources available in the world, the bulletin said.
The hospital has said he is expected to have a stormy course in the "next 24 hours" due to the complications caused by re-warming and establishment of blood flow to the cold parts of the body.
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He was then transferred to Delhi by a fixed-wing aircraft of IAF along with a critical care specialist of the force and a medical specialist from the base camp.
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Hailing Hanamanthappa's "endurance and will power" to serve the nation, Congress President Sonia Gandhi wished for his speedy recovery.
"I join the nation in praying for the speedy recovery of Lance Naik Hanamanthappa. We salute his endurance and will power to serve the nation," she said.