"The Prime Minister assured us he would speak to President Musharraf on the issue and that the government would do all it could to save the life of Indian national Sarabjit Singh," Shamsher Singh Dullo said, a senior leader of the Congress party.
"We urged the Prime Minister to do everything possible to save an innocent. Why should he be punished for mistaken identity?" Dullo said, according to the Press Trust of India news agency.
The family said he was not the Manjit Singh, who the Pakistani authorities want for a series of bombings in Lahore in 1990.
The Indian foreign ministry too moved to formally seek details of Singh.
Spokesman Navtej Sarna said India's "high commission in Islamabad had taken up the matter and sought consular access" to Singh to determine his nationality and other details.
Singh, from the border village of Bikhiwind in Indian Punjab state, went missing in 1990 when he strayed across the border, his sister Dalbir Kaur said.
Once in Pakistan, he was mistaken for a spy of the Research and Analysis Wing (RAW), India's external intelligence agency, and arrested for allegedly masterminding the bomb blasts in Lahore, she said.
Later a Pakistani lower court sentenced him to death, a ruling upheld by the Supreme Court last week. No date has been set for the execution of the man, who was tried under the name of Manjit Singh.
"My brother is innocent," his sister told reporters. "He's a straight-forward person and not a RAW agent. He strayed across the border while inebriated."
The issue is likely to come up when Indian foreign secretary Shyam Saran travels to Islamabad next week for a meeting of South Asian officials.