India said "this is not the time for invoking legal and bureaucratic reasons for not taking the right steps to save a human life."
"We are concerned at the condition of Sarabjit Singh indicated by reports made available by doctors treating him in Jinnah Hospital," said a statement issued here by the external affairs ministry.
Sarabjit, 49, had suffered critical head injuries after unprovoked and sudden assault by four to five prisoners April 26 in the Kot Lakhpat jail.
Singh is undergoing treatment in Jinnah hospital in Lahore. He has been on ventilator life support since. Doctors have reportedly indicated that he was "clinically dead."
In this regard, Indian High Commissioner to Pakistan Sharat Sabharwal met Pakistan Foreign Secretary Jalil Abbas Jilani, the statement said.
"Our high commissioner has met the Pakistan foreign secretary and urged the government of Pakistan to immediately release Sarabjit Singh on humanitarian and sympathetic grounds so that he can benefit from the best available treatment in India," it said.
"Alternatively we have also proposed that Sarabjit Singh should be sent to a third country for proper medical treatment," the statement added.
"This is not the time for invoking legal and bureaucratic reasons for not taking the right steps to save a human life.
"We believe that every endeavour should be made to save his life," the statement said.
Sarabjit has been on death row in Pakistan since 1990 after being convicted by Pakistani courts for bomb blasts in Lahore and Multan, which left 14 people dead.
Sarabjit's family claims he is innocent, and was arrested when he crossed over to Pakistan in an inebriated state.
Police in Pakistan, however, claimed that Sarabjit Singh, known as Manjit Singh, was involved in terrorist strikes.
His family, including his two daughters and wife, returned to India Wednesday.
They held both the Indian and Pakistan governments responsible for Singh's worsening condition and said they will pursue the case with Prime Minister Manmohan Singh, Congress President Sonia Gandhi and others.
The distraught family said Manmohan Singh should quit for having failed to save Sarabjit.