A bench of Justices Vipin Sanghi and Rajnish Bhatnagar issued notices to the Centre and Delhi government and Delhi Police and asked them to take instructions on the matter.
The bench, thereafter, suggested that the ministry can continue processing the suggestions, while keeping the window open for some further time to receive more.
The MP CM who is in Delhi since Sunday has been holding meetings with top leadership of the party, including national president JP Nadda, union home minister Amit Shah.
It will be the second state-run hospital in Delhi to get the facility after LNJP Hospital, where the facility was inaugurated by Chief Minister Arvind Kejriwal on Thursday.
According to Dr Abhimanyu Sardana, the president of Residents' Doctors Association of Hindu Rao Hospital, the protest is to demand proper segregation of the donning and doffing area.
In Northwest district, where the exercise has been concluded, there has been a rise in the number of containment zones from 21 to 28, an official said.
The official had last visited the court premises on June 19 and had come in contact with the personal assistant posted in the judge's court, said the circular.