Talking to reporters in Rashtrapati Bhawan, Mr Shinde said he is closely looking at the recent developments and some action may be in the offing.
Asked if recent reports of Delhi Police Commissioner Neeraj Kumar's likely removal were true, Mr Shinde said, "I have ordered an inquiry into the two recent incidents - what happened to Mamata Banerjee at the Planning Commission and the case of some people entering my house. Action will be taken against those found responsible for it."
However, he did not specify who will face action and said he will wait for the inquiry report.
Both the inquiries are being conducted by Additional Secretary Khurshid Ahmed Ganai of the Home Ministry.
Meanwhile, Delhi Lieutenant Governor Tejinder Khanna said all cases of missing children in the capital will be treated as cases of kidnapping, which being an offence will require a more serious approach from the police.
Asked about the brutal rape of a five-year-old, Mr Khanna said the accused Manoj Kumar, has been arrested from Muzzafarpur.
He said Assistant Commissioner of Police BS Ahlawat, who had slapped a girl protesting against the crime, had taken this action as she had allegedly pushed and heckled Delhi Health Minister AK Walia. He maintained that the news channels were showing only a part of the clipping. Mr Ahlawat has been suspended.