"To resign or not to resign is left to him. Government cannot do anything within the purview of the law on the issue," he told reporters in Ballari, when questioned about the demand for the exit of Rao.
Siddaramaiah dismissed allegations that the government was protecting Rao, who is in the eye of a storm over the alleged extortion racket to which his son has been linked.
Meanwhile, various organisations including the local lawyers association and Aam Aadmi party workers today staged protests in various parts of Bengaluru demanding resignation of Rao.
Opposition parties have been pressing for a CBI probe into the scandal and initiated the process to move a motion in the legislature for the removal of Rao.
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The government has ordered setting up of the Special Investigation Team (SIT) into the alleged corruption by some Lokayukta officials and Rao's son.
The institution was rocked by the alleged scandal recently after its Superintendent of Police Sonia Narang wrote a letter to its Registrar, about the complaint she received from a person, who alleged that someone from the Lokayukta office demanded Rs 1 crore in bribe to avoid a raid.