Afzal Guru, 43, was executed Saturday at Tihar Prison outside New Delhi. Following a tradition inherited from India's British rulers, his body was buried at the prison.
Mohammed Yasin, a cousin, said the family rejected an offer from Home Secretary R.K. Singh to allow the family to pray at the grave site, the Press Trust of India reported. He said the family would only come to the jail to bring Guru's body home.
"We don't understand what they mean," Yasin said. "We can pray even from here. We want the body to be handed back, nothing less than that."
The family is from Sopore in the disputed Jammu and Kashmir region. Guru was arrested shortly after the 2001 attack on Parliament carried out by the Lashkar-e-Toiba and the Jaish-e-Mohammad groups and was convicted and given a death sentence the next year.
Yasin also called it a "cruel joke" that the family only received a letter Monday notifying them of the impending execution. Authorities have said the letter was delayed because of the weekend.
He accused authorities of using his cousin's body for political purposes.
"Afzal was hanged -- rightly or wrongly, we don't want to go into that -- but politicians should stop playing politics," he said.