"We are inclined to modify the said condition, while other conditions will stand," a bench comprising Chief Justice P Sathasivam and Justice Ranjana Prakash Desai said.
The bench took into consideration that the trial of the case has been shifted to Mumbai and the case was committed to sessions court after the apex court's September 27, 2012 order.
It also noted that Shah has been elected to the Gujarat Assembly and he had been appointed as the General Secretary of BJP.
In response to his application, CBI only said there was an apprehension that as an influential person, he may influence or threaten the witnesses.
The apex court had earlier rejected CBI's plea to cancel bail granted to former Minister Shah by the Gujarat High Court but had agreed to transfer the case to Mumbai to preserve the integrity of the trial. The bench had imposed strict conditions on Shah and had made it clear that the relief granted in the Sohrabuddin case will not be extended to him in the Tulsiram Prajapati killing case.
The apex court had directed Shah to give an undertaking in writing to the trial court that he would not commit any breach of conditions of the bail bond and would not try to influence any witnesses or tamper with the prosecution evidence in any manner and report to the CBI office every alternate Saturdays at 11.00 am.
The bench had warned that in case Shah commits any breach of conditions of the bail bond or the undertaking given to the court, it will be open to the CBI to move the trial court for cancellation of his bail.
Sheikh and his wife Kauser Bi were allegedly abducted by Gujarat's Anti-Terrorist Squad (ATS) from Hyderabad and killed in a fake encounter near Gandhinagar in November 2005.
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