Hospitals in the city are in crisis, with intensive care beds full and an acute shortage of medical oxygen.
Delhi's government wants the army to run Covid care facilities and intensive care units.
Across India, case numbers since the start of the outbreak are closing in on 20 million.
The country has seen more than 300,000 new cases a day for nearly two weeks straight while deaths stand at 220,000.
Experts say total Covid cases and deaths in India are likely to be much higher, citing lack of testing and patients dying at home without being seen by doctors.
Delhi, which this weekend reported record daily deaths at more than 400, wants the army to run medical care with oxygen facilities for around 10,000 patients, and a further 1,000 intensive care units.
Deputy Chief Minister Manish Sisodia said that with healthcare "overwhelmed... it will be a timely help to the people of Delhi if the Ministry of Defence, with the considerable resources at its command, is tasked with the responsibility to provide and man the additional Covid health facilities".
Delhi Chief Minister Arvind Kejriwal has repeatedly said that the city is not getting enough oxygen from the federal government, which allocates oxygen quotas to states.
But federal officials deny there are shortages, saying the challenge has come from transportation.
India produces thousands of tonnes of oxygen a day, but some experts say the supply crunch comes from a lack of investment in distribution networks.
Delhi hospitals have resorted to sending SOS messages on social media to secure supplies. For residents, hours spent in queues to top up portable canisters have become part of daily life.
"It's a battle we are fighting every day," said Dr Gautam Singh, who runs the Shri Ram Singh hospital.
"Half of my hospital staff are on the road with cylinders to get them filled every day, going from one place to another."
There are severe strains outside of the capital too. In the southern state of Karnataka, 24 people died in one hospital, but the government there has denied reports that all of them died due to a shortage of oxygen.