Mohammed Afzal sentenced to death for his part in the Parliament attack was due to be hanged at 6 am on Friday.
"Since his petition is pending before the President, the hanging will not take place on Friday," Onkarmal Kedia, Home Ministry spokesman, said.
As per the law, the President can pardon people sentenced to die, but in the past, not many mercy petitions have been granted.
Kashmiri leaders have said the execution would fuel a revolt in the Valley. There have been several protests in Kashmir against the execution and the issue has been a hot topic of debate by political parties.
Former Chief Minister of Jammu and Kashmir, Farooq Abdullah, had said earlier that India will "go up in flames" if Afzal was hanged.
Separately, Afzal's lawyers said they will approach the Supreme Court in a final attempt to prevent the execution, arguing his conviction was flawed.
"We will argue that he can not be hung merely on the grounds that his execution will satisfy the collective conscience of the nation," Nandita Haksar said.