Prime Minister Narendra Modi's Hindu-nationalist Bharatiya Janata Party, which runs Assam state where the National Register of Citizens (NRC) was collated, had asked for the list, saying it was necessary to detect "foreign infiltrators".
Its critics said the NRC process reflected the BJP's goal to serve Hindus, 80% of the Indian population, with many of those excluded expected to be Muslim.
Janata Dal United party vice-president Prashant Kishor called the NRC a "botched up" process, remarking that it leaves people as "foreigners in their own country".
A member of a BJP allied-party, Kishor's tweet was comparatively long, and read, "Such is the price people pay when political posturing & rhetoric is misunderstood as solution for complex issues related to national security without paying attention to strategic & systemic challenges."
Local BJP leaders claim that many Bengali-speaking Hindus were left off the list. This would not endear traditionally left-wing, Congress or regional party voters to switch to the BJP which is picking off the control of one state after another.
Ranjeet Kumar Dass, the BJP party president in Assam told the Press Trust of India late Saturday that, "We do not trust this NRC... Many people with forged certificates were included," while 200,000 people he called "genuine Indians" were left out.
Those left off have 120 days to appeal at special Foreigners Tribunals.
Many of those whose names do not appear on the lists are poor and illiterate. They are faced with having to take on a lengthy and expensive legal process.
West Bengal State's chief minister Mamata Banerjee of the opposition All India Trinamool Congress called the NRC a "fiasco".
A leader of the main opposition Congress party Adhir Ranjan Chowdhury said his party would support those who were wrongly excluded, including providing them with legal aid.
United Nations High Commissioner for Refugees Filippo Grandi on Sunday called on the Indian government in New Delhi to refrain from detaining or deporting anyone whose nationality is not verified through the process.
"Any process that could leave large numbers of people without a nationality would be an enormous blow to global efforts to eradicate statelessness," Grandi also said in a statement.
Assam in the north-east of India shares short external borders with Bangladesh and Bhutan and has been subject to population inflows such as in 1971 when masses of East Pakistanis fled at the time of the independence war which led to the creation of Bangladesh.
The people included on the NRC were to have been only those who could prove they or their forebears were in India before 1971.
India's political demography
Just before the results of the NRC, New Delhi revoked the autonomy of Kashmir, India's only Muslim-majority state. This has reinforced fears among India's 170 million Muslim minority that they are being singled out by the central government.