He had sought 30-day bail citing his wife's ill-health.
Justice A S Supehia, however, granted him a one-week bail.
Bajrangi is lodged at Sabarmati Central Jail here. He was convicted by a special fast track court in 2012 for his role in the post-Godhra violence at Naroda Patiya here in 2002, and sentenced to life imprisonment till death.
Former Gujarat minister Maya Kodnani too was convicted in the case. Ninety-six people had died at Naroda Patiya in one of the worst massacres of post-Godhra Gujarat riots.
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