"Trial is going on in the court, which is independent. It is for the court to take a decision (on expediting the trial). The government has no role in the matter," Rupani told reporters while replying to queries on the sidelines of a function in Rajkot.
He rejected the Congress' allegations that the ruling party was trying "shield the accused".
Senior Congress leader Shaktisinh Gohil welcome the Supreme Court's observations and voiced hope that the BJP government will act to ensure that the guilty are punished.
"Law and order is a state subject. This is not the first time it has happened. Ever since the BJP came to power, it had to repeatedly face the ire of the Supreme Court," he said.
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"It's the government's responsibility to ensure the accused get punished as early as possible. We welcome what the Supreme Court said and hope this will make the government act."
After giving directions, a bench, comprising justices N V Ramanna and Amitava Roy, posted the matter for further hearing after Diwali.
Two Surat-based sisters had lodged separate complaints against Asaram and his son Narayan Sai, accusing them of rape and illegal confinement, among other charges.
Also, in Rajasthan, a teenage girl had accused Asaram of sexual assault at his ashram near Jodhpur.
The apex court had noted that trial in the matter was unnecessarily prolonged and the prosecution witnesses were being attacked, which led to the death of two witnesses.