He stated that such cases were bringing "dishonour to the families, the community and the country."
"Whoever is the cause of the crime, an individual or a collective, must be punished. Once the law is made, it must be enforced. Those involved must be punished," said Chidambaram.
Speaker Meira Kumar too expressed serious concern over the growing incidents saying young people were being killed by their family members.
But former Bihar Chief Minister Lalu Prasad said that an all-party meeting should be commenced by the government on the "sensitive" issue involving castes.
However, describing honour killing as murder, Home Minister said, "the government is actively considering a proposal to amend the existing law or to enact a separate law" to tackle such crimes.