Here are the top 10 Points in this big story:
The date of inauguration has also irked the Congress. May 28 is the birth anniversary of VD Savarkar, one of the BJP's biggest icons, and the Congress said the selection of the date is a "complete insult" to the country's founding fathers.
"Congress has a habit of raking controversies where none exist. While President is the Head of State, PM is the Head of Govt & leads the Parliament on behalf of the Govt, whose Policies are effected in form of Laws. The President is not a Member of either House, whereas PM is," tweeted Union minister Hardeep Singh Puri.
BJP spokesperson Gaurav Bhatia called the Congress "useless" and said, "Veer Savarkar is the pride of every Indian. Those who are questioning the date, tell them that they are inconsequential, not even worth the dust on Veer Savarkar's feet".
Congress chief Mallikarjun Kharge has accused the government of "repeatedly disrespecting propriety" by not inviting the President and the former President to the inauguration.
"While Former President, Shri Kovind was not invited for the New Parliament foundation laying ceremony… The President of India Smt. Droupadi Murmu is not being invited for the inauguration of the new Parliament Building," Mallikarjun Kharge tweeted.
"She (the President) alone represents government, opposition, and every citizen alike. She is the First Citizen of India. Inauguration of the new Parliament building by her will symbolise Government's commitment to Democratic values and Constitutional propriety," read another of his tweets.
Other opposition parties have also slammed the government over the inauguration. "Obsession with self-image and cameras trumps decency and norms when it comes to Modi-ji," said CPI's D Raja.
"He (PM Modi) is head of the executive, not legislature. We have separation of powers and Hon'ble Lok Sabha Speaker and Rajya Sabha Chair could have inaugurated (it). It's made with public money, why is PM behaving like his 'friends' have sponsored it from their private funds," tweeted AIMIM chief Asaduddin Owaisi.
The Opposition plans to calibrate their stance regarding the opening at a mega meeting they are planning.
The new Parliament building can comfortably seat 888 members in the Lok Sabha chamber and 300 in the Rajya Sabha chamber. In case of a joint sitting of both Houses, 1,280 members can be accommodated in the Lok Sabha chamber.
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