"Police should not come under any pressure while conducting investigation and it will not happen. Strict action will be taken based on the outcome of the probe," he told reporters after apprising Home Minister Sushilkumar Shinde about the progress in the case.
The chief minister said saints should maintain sanctity in society so that there is no scope of raising fingers aggainst them.
"I have already said no one is above law and law should take its own course," Gehlot added.
Asaram has been accused of molesting a minor girl in Rajasthan.
The victim filed a complaint at a police station in New Delhi Aug 20 accusing Asaram of sexually assaulting her at his ashram in Jodhpur city.
A first information report (FIR) was also registered against Asaram in Jodhpur the following day.
Asaram has been booked under various sections of the Protection of Children from Sexual Offences Act and the Indian Penal Code.
Rajasthan Police have also initiated formalities to get a look-out circular issued against the spiritual guru so that he could not leave the country.
The victim's father has demanded a Central Bureau of Investigation (CBI) probe into the matter.
The issue has rocked the Indian parliament and has led to public protests.
Although, political parties have demanded strict against Asaram, the Bharatiya Janata Party's Uma Bharti has sprung to his defence.
Attacking the BJP for its "double standards", Congress general secretary Digvijaya Singh said : "Death penalty to others but pardon to fake god men."
"Double standards of BJP on crime against women," he tweeted, without naming Asaram.
The BJP has been demanding, inside and outside the parliament, the death penalty for rapists.
The spiritual guru has denied meeting the girl alone. "It is completely false," he has told a news channel.
--IANS (Posted on 28-08-2013)