The rule comes after Bhullar's family requested that he should not be executed as he is mentally unwell.
In April last year, the Supreme Court had refused to commute his death sentence to life imprisonment on the grounds of mental illness and a delay by the President of India in deciding his clemency appeal.
Bhullar was convicted and awarded death penalty for triggering a bomb blast in New Delhi in September 1993, which killed nine persons and injured 25 others, including then Youth Congress president M S Bitta
Last week, in a landmark verdict, the court commuted the death sentences of 15 prisomers and ruled that "inordinate and inexplicable" delays in carrying out an execution were grounds for reducing the penalty.
The court clarified that delays needed to be "inordinate" and "inexplicable", but it also said that mental illness such as schizophrenia and the use of solitary confinement could make a convict eligible for a reduced sentence.
(With PTI inputs)