BJP spokesperson Ravishankar Prasad described the incident as a "great pain, great agony and great distress."
"We outrightly condemn it. Why is the government not taking action? The incident has happened right in the heart of the capital, adjacent to India Gate and outside a gate of the Delhi High Court. There is no security and there is no intelligence beef-up," he told reporters.
He said the blast was "deeply regrettable" and said the government should answer how many innocent civilians would have to die in the country due to terrorist attacks.
"Terrorists come with impunity and kill people with impunity," he said.
CPI National Secretary D Raja said the party "strongly condemns" the blast and asked the government to explain why such terror attacks keep happening in the country.
"The government should initiate a thorough probe into the incident and they should say whether it was a failure of the intelligence agencies or failure of the policy adopted by it with regard to terror," he said.
"The government should answer. No person involved in such attacks should go scot-free. I think there is a failure on the part of the government particularly the Home Ministry," he said.
Janata Party president Subramanian Swamy demanded that Home Minister P Chidambaram resign in the wake of the incident.
"The UPA Government has failed to formulate a counter-terrorist strategy. I also demand that the Prime Minister cancel his visit to Bangladesh forthwith," he said.