"In some earlier such incidents, including in Hyderabad, wrong people were caught, sent to jail for several years and released later by the courts," CPI(M) General Secretary Prakash Karat told reporters here.
He said proper investigations should be carried out and the real culprits brought to book.
Separately, in a statement, the party's Politburo said "given past experience, there should be no preconceived notions about those who have committed this crime. There has to be a careful investigation to ascertain those responsible for this attack and to bring them to justice."
"This is the time to show unity, create confidence among the people to face the challenge of mindless murders and terrorism," it said, urging the people of Hyderabad to face the challenge with calm and courage.
Both parties condemned the twin bomb blasts and conveyed their heartfelt sympathies to all those families who have suffered grievous losses.