The killers were supposed to be hanged on Sep 9.
The Tamil Nadu assembly adopted a resolution seeking clemency for the killers.
Janata Party President Subramanian Swamy reacting on the whole issue said, "The stay is inconsistent to the Supreme Court judgement in 1990."
"Stay can't be given if the President has given a go ahead for execution.This should be clarified in SC. There cannot be any pardon for anti-nationals. Attorney General should get the stay vacated.
"When a murder takes place, it's not a question of personal enmity but it is against the state," he added.
Earlier DMK Supremo M Karunanidhi pleaded to Congress President Sonia Gandhi to forgive the assassins keeping in mind the sentiments of the Tamils.
Karunanidhi also said that had Rajiv Gandhi been alive, he would have forgiven the convicts.
"Had young leader Rajiv Gandhi been alive today, that noble man would have definitely come forward to save the lives of Santhan, Perarivalan and Murugan, responding to the voice of true Tamils and in accordance with the golden saying of Anna, ''forget and forgive", Karunanidhi had said in a statement.
"If this is done, the entire Tamil race will extol such humanitarian action and they will be happy," he added.
Jayalalithaa, Chief Minister, Tamil Nadu on the issue said that she had no right to intervene on the orders given by President Prathiba Patil who had earlier rejected the mercy plea of the three convicts.
Various political parties also appealed for clemency for the three.