The leaders lead all MPs to the new Parliament building after a function that lasted nearly an hour and half.
Parliamentary Affairs Minister Pralhad Joshi said a total of eight bills have been listed for consideration and passage during the session
The session is likely to see the proceedings of Parliament moving from the old building to the new Parliament building.
The Data Protection bill seeks to protect the privacy of Indian citizens while the Delhi Services bill gives the Central government control over bureaucrats in the Delhi government.
This is in contrast to a Supreme Court judgment of March which said the panel should comprise the prime minister, the leader of the opposition in Lok Sabha and the Chief Justice of India.
The TMC leader sought to speak under the pretext of raising a point of order.
The Delhi chief minister said the bill was an insult to the right to vote of the people of Delhi.
The Government of National Capital Territory of Delhi (Amendment) Bill, 2023, has already been passed by Lok Sabha.
This move will cut off the Rajya Sabha's authority to reject the bill through voting.
he Rajya Sabha was adjourned for the day on Monday as the opposition insisted on discussing the Manipur issue under Rule 267 of the House.