Besides, the relentless cases of crime against women in the national capital have raised big concern for the authorities.
Speaking to the reporters at the Rashtrapati Bhavan, the minister said he was closely monitoring the recent developments in Delhi and that some action might be in the offing.
When asked if reports of likely removal of Delhi Police commissioner Neeraj Kumar were true, Shinde said he had ordered inquiry into the recent protests against Banerjee and some people trying to enter his house.
He said action would be taken against those found responsible for these instances. People protesting against the recent instance where a five-year-old child was kidnapped and brutally raped have also been demanding the resignation of Kumar.
The commissioner has been under stress since the brutal gangrape and assault of a 23-year-old woman in the national capital in a moving bus last December, which had shocked the entire nation and also sent a rippling effect abroad.
Shinde, however, did not specify who would face the action and said he will wait for the inquiry report. Both inquiries are being conducted by additional secretary Khurshid Ahmed Ganai of the home ministry.
The person accused of raping the five-year-old in east Delhi, Manoj Kumar, was arrested from Muzaffarpur in Bihar.