In a meeting with Prime Minister Narendra Modi, the Chief of Defence Staff General Bipin Rawat said oxygen would be released to hospitals from armed forces reserves and retired medical military personnel would join Covid-19 health facilities.
Where possible, military medical infrastructure will be made available to civilians, a government statement said, as new coronavirus infections hit a record peak for a fifth day.
Virologists said more infectious variants of the virus, including an Indian one, have fuelled the resurgence.
Hospitals and doctors in some northern states posted urgent notices saying they were unable to cope with the influx.
In some of the worst-hit cities, bodies were being burnt in makeshift facilities offering mass cremations.
The southern state of Karnataka, home to the tech city of Bengaluru, ordered a 14-day lockdown from Tuesday, joining the western industrial state of Maharashtra, where lockdowns run until 1 May, although some states were also set to lift lockdown measures this week.
The patchy curbs, complicated by local elections and mass festival gatherings, could prompt breakouts elsewhere, as infections rose by 352,991 in the last 24 hours, with crowded hospitals running out of oxygen supplies and beds.
"Currently the hospital is in beg-and-borrow mode and it is an extreme crisis situation," said a spokesman for the Sir Ganga Ram Hospital in the capital, New Delhi.
Modi on Sunday urged all citizens to get vaccinated and to exercise caution amid what he called a "storm" of infections.
Inoculations peaked at 4.5 million doses on 5 April but have since averaged about 2.7 million a day, government figures show.
The situation in India is "beyond heartbreaking" and the World Health Organisation is sending extra staff and supplies there to help fight the pandemic, WHO chief Tedros Adhanom Ghebreyesus said on Monday.
"WHO is doing everything we can, providing critical equipment and supplies, including thousands of oxygen concentrators, prefabricated mobile field hospitals and laboratory supplies," Tedros told a briefing.
He said he had already announced 2600 extra WHO staff members were going to India to help support the effort to fight the disease.
On Sunday, President Joe Biden said the United States would send raw materials for vaccines, medical equipment and protective gear. Germany joined a growing list of countries pledging supplies.
In Moscow, which expects 50 million doses of its Sputnik V vaccine to be made each month in India this summer, a Kremlin spokesman expressed concern over the situation. Russian pharmaceutical firm Pharmasyntez said it was ready to ship up to 1 million packs of the remdesivir antiviral drug to India by the end of May, once it has received the approval of Russia's government.
India, with a population of 1.3 billion, has an official tally of 17.31 million infections and 195,123 deaths, after 2,812 deaths overnight, health ministry data showed, although health experts say the figures probably run higher.
Several cities have ordered curfews, while police enforce social distancing and mask-wearing.
Politicians, especially Modi, have faced criticism for holding rallies during state election campaigns that draw thousands into packed stadiums.
About 8.6 million voters were expected to cast ballots on Monday in the eastern state of West Bengal, in the final phases of a contest set to wrap up this week. Also voting in local elections was the most populous state of Uttar Pradesh, which has been reporting an average of 30,000 infections a day.
Vaccine demand has outpaced supply as the inoculation campaign widened this month, while companies struggle to boost output, partly because of a shortage of raw material and a fire at a facility making the AstraZeneca dose.
However, the federal government will not import vaccines itself but expects states and companies to do so instead, in a step aimed at backing domestic manufacturers, two government officials told Reuters.
Neighbouring Bangladesh sealed its border with India for 14 days, its foreign ministry said, though trade will continue. Air travel has been suspended since Bangladesh imposed a lockdown on 14 April to combat record infections and deaths.