The prime minister is resisting the move due to the economic impact.
India added more than 355,000 cases on Tuesday, down from more than 400,000 daily infections on 30 April.
The government says cases are "slowing down", but testing numbers have also dipped, meaning the true caseload could be far higher.
Confirmed infection numbers have however been consistently falling in Maharashtra state, which has driven the second wave since early April.
The decision to impose restrictions in India is made by individual state authorities, rather than the central government. Prime Minister Narendra Modi has said that states should only consider restrictions as "a last option."
But there are increasing calls for a second national lockdown coming from senior politicians, business leaders, international health experts and India's main opposition Congress party.
Rahul Gandhi, the senior Congress leader, said there was no other way to stop the spread of the virus, tweeting: "A crime has been committed against India."
Dr Anthony Fauci, America's top public health expert, described the situation as "extremely serious" and said a nationwide lockdown is needed, as well as a massive vaccination drive and the construction of makeshift hospitals.
Last year, Narendra Modi was heavily criticised after imposing a nationwide lockdown with less than four hours' notice. It caused a devastating humanitarian crisis as tens of thousands of migrant workers were left without work and forced to walk hundreds of kilometres to their native villages.
The lockdown saw India's economic output fall by a record 24% between April and June 2020 compared to the same period a year earlier, and the government has said another national lockdown would have dire consequences for the country's economy.
But business leaders have joined the calls for the measure. Members of India's Covid-19 taskforce which advises the central government are "pushing hard" for a two week lockdown, The Indian Express reported, citing an anonymous member.
"A nationwide lockdown rather than what we are doing now, in bits and pieces across states, because of the simple fact that it is spreading all over," they are quoted as saying.
Many states have introduced restrictions, from full lockdowns to night curfews. The northern state of Bihar, which has been adding about 13,000 daily cases in recent days, is the latest to announce a full lockdown -only essential services, such as government offices, groceries and hospitals, will be open.
The capital, Delhi and financial hub, Mumbai, are also currently under restrictions.
Meanwhile an oxygen shortage has shown no signs of abating and people in several hotspot cities, including Delhi, are struggling for treatment.
India's second wave, fuelled by lax safety protocols and massive public festivals and election rallies, has overwhelmed its hospitals. Delays in testing, diagnosis and treatment, as well as a shortage of critical care beds and crucial drugs, has resulted in a spike in deaths.
The country has so far reported more than 222,000 deaths due to the virus. But experts say India's Covid death toll is vastly under-reported as official tallies don't appear to match what people are witnessing on the ground - long lines at crematoriums, mass funeral pyres and cities running out of space to bury or cremate the dead.