Congress' chief spokesperson Randeep Singh Surjewala said "every Indian must condemn this mindless act" of the government.
UIDAI Deputy Director BM Patnaik has informed the police that an input was received from The Tribune newspaper that it had purchased a service being offered by anonymous sellers on WhatsApp that provided unrestricted access any of the more than 1 billion Aadhaar numbers, according to the police.
The FIR mentions the names of the journalist and the people the reporter reached out to purchase the Aadhaar data, but they have not been shown as accused, the police said.
The Congress also raised questions on the Modi government's "intentions" on privacy issues as it referred to former Attorney-General Mukul Rohatgi reportedly saying last year that "no citizen can have an absolute right over his/her body". It charged the government with being "dismissive and oppressive" instead of being "responsive" to issues flagged.
"Intent, & 'Intentions' of Modi Govt on Privacy were thoroughly exposed when it had proclaimed that 'no citizen can have an absolute right over his/her body'," Congress' chief spokesperson Randeep Singh Surjewala said in a tweet.
"In SC, Modi Govt had accepted Aadhaar data leak! Now instead of investigating, an evasive Modi ji shoots the messenger!" he added.
Addressing a press conference here, party spokesperson Shobha Oza said the Unique Identification Authority of India (UIDAI) filing the FIR in connection with the report showed the government's "dictatorial mindset".
She said "from time to time" there have been reports about Aadhaar data leakage and referred to a study by the Bengaluru-based organisation - Centre for Internet and Society (CIS), which in May last year claimed that information about 130 million card holders had been leaked from four government websites.
She alleged that personal information of India's citizens were exposed to hackers every day and the right to privacy was being "mocked and flouted with impunity".
"But the Modi government remains immune...the government itself has accepted that there is a leakage. But still the government is being adamant, which is a matter of concern," Ms Oza said.
Under fire for filing the FIR, the UIDAI said it respects free speech, including freedom of the press, and its police complaint should not be viewed as "shooting the messenger".
In a statement, it said that its act should not be viewed as one targeting the media or a whistle blower.
Ms Oza also defended senior Congress leader P Chidambaram for suggesting that the government's "militaristic" approach allegedly failed to end terrorism in Jammu and Kashmir.
In a series of tweets, Mr Chidambaram today suggested that the government's "muscular and militaristic approach" had failed in Jammu and Kashmir. The former Union minister also pitched for the government to find out a political solution to the Kashmir issue, and said former Prime Ministers AB Vajpayee and Manmohan Singh will be remembered for their "diligent efforts" to find a solution to the issue.
Mr Chidambaram also said that the "mandate" of Dineshwar Sharma as Special Representative for Kashmir was "not clear".
Stressing that Kashmir was an integral part of India, Ms Oza said the state had moved towards normalcy during the previous government, led by her party. However, she alleged, the situation worsened since the PDP-BJP government was formed in the state and asked the BJP to come clear about it.
"Peace has to be restored in Jammu and Kashmir. Citizens of Jammu and Kashmir are citizens of India... The government has to take strict measures to ensure normalcy and peace there," she said.
Ms Oza also slammed the government over Union minister Ramdas Athawale saying that Gujarat MLA Jignesh Mevani was not responsible for the violence in Maharashtra's Bhima-Koregaon last week even though an FIR was lodged against him for a "provocative speech", which led to clashes.
"We have seen them (the ruling BJP) appointing those spitting communal venom as chief minister. But the government (led by the BJP) does not shy from lodging FIR against innocent people," she added.