Burney's comments came in the wake of the death of a Paksitani prisoner in a jail in India.
Burney, who is also campaigning for Indian death row prisoner Sarabjit Singh's death sentence to be commuted to life imprisonment, said there are 50 Pakistani prisoners in Amritsar jail who had already completed their sentences.
Burney said he had decided to visit India before the end of this month to work for the release of these prisoners after Mohammad Asif, 32, died suddenly on his way from Amritsar jail to hospital following a sudden deterioration in his health.
Indian officials have said Asif was suffering from tuberculosis. The Ansar Burney Trust is working to bring Asif's body back to Pakistan.
Burney spoke with Indian high commissioner Satyabrata Pal and visa counsellor Suresh Reddy, who told him the body would be returned to Pakistan as soon as
possible after the completion of formalities.
Asif was convicted last year for violating the Indian Passport Act and had served his sentence in Gurdaspur Jail, from where he was shifted to Amritsar Jail.
The Pakistani High Commission in New Delhi had been provided consular access to Asif and he was to have been repatriated this month.
During his visit to India, Burney is expected to meet senior officials, including the ministers for home affairs and external affairs, and human rights activists in an effort to secure the release of all Pakistani prisoners who had completed their sentences.
According to the Ansar Burney Trust, a prisoner named Abdul Sharif had been sentenced to a month's imprisonment by an Indian court but had spent the past 10 years in jail. He is currently being held in the Amritsar transit camp, the Trust claimed.
"This is the reason I have decided to go to India to meet Indian authorities and make a request in the name of human rights for the immediate release of all such Pakistani prisoners who have already completed their sentences long ago," said Burney.