During a meeting with Indian President KR Narayanan, Mrs Gandhi asked him to commute the death sentence placed on the only woman convicted of killing her husband in 1991.
Mohini Giri, the head of a Delhi-based non-governmental organisation, told the BBC that Mrs Gandhi had made the appeal because the woman, S Nalini, is the mother of a young child.
It is believed that Mrs Gandhi asked for the death sentence to be commuted to life imprisonment.
Ms Nalini, along with three men, was sentenced to death last year for Mr Gandhi's assassination.
Following several failed clemency appeals, the execution was scheduled for 5 November, but it was postponed following a fresh appeal which is currently under review in the southern city of Madras.
Controversy
Earlier, the governor of the southern state of Tamil Nadu, Fatima Beevi, rejected clemency petitions from the four people sentenced for the assassination.
The issue has aroused debate in India, with political parties divided over the petitions.
Tamil Nadu's Chief Minister, Mr Karunanidhi, has spoken out against the death penalty, saying a life sentence would give the guilty a chance to reform.
But his comments were attacked by opposition parties which want the sentence carried out.
Day that shocked India
Rajiv Gandhi was killed at a campaign rally in May 1991, by a suspected female Tamil Tiger suicide bomber who had strapped explosives to her waist.
The assassination shocked India and an immediate investigation was launched.