Lance Naik (Corporal) Hanamanthappa Koppad was trapped under 8m of snow at a height of nearly 6,000m along with nine other soldiers who all died.
An army statement said that Mr Koppad "continues to battle the odds" and remains "ventilator dependent".
The avalanche hit an army post on the glacier's northern side last Wednesday.
Siachen is patrolled by troops from both India and Pakistan, who dispute the region's sovereignty. It is also known as the world's highest battlefield.
An Indian soldier who was buried for six days in an avalanche on the Siachen glacier in Indian-administered Kashmir remains "very critical" in hospital.