He asked people to work collectively to uproot such depravity from the society.
"It is widely accepted that, as a country, we have vast improvements to make in these (safety, security and status of women) areas. These issues came into sharper focus after the horrific gangrape incident in Delhi last December.
"The gruesome assault on a little child a few days back reminds us of the need to work collectively to root out this sort of depravity from our society," Singh said.
The Prime Minister said the agitations that have followed the two incidents also point to the need for showing concern and sensitivity while dealing with public anxiety that such incidents generate.
"Our government has moved with speed in strengthening the law to be able to deal more effectively with offences against women. However, this is but a small part of what needs to be done.