Talking to reporters here, Chavan said he would take action regarding the arrest of the two girls once he received the report from the police officer who has been asked to probe the entire episode which evoked sharp criticism.
"I have instructed an inquiry to be conducted by a very senior officer immediately. I will act as soon as I receive the report," he said.
The Chief Minister said he expected to get the report by Wednesday (tomorrow).
Two girls - Shaheen Dhada and Renu - were arrested in adjoining Thane district on Sunday over their post on the popular social networking site opposing the shutdown in Mumbai for Shiv Sena chief Thackeray's funeral. They were later granted bail.
The probe report would highlight how an IPC section like 505(2) (that pertains to statements which create or promote enmity, hatred or ill-will between classes) had been slapped against the girls and who was responsible for their arrest, the Chief Minister said.
The arrests had sparked an outrage with Press Council of India chief Markandey Katju demanding "immediate" action against the police personnel involved in the arrest of the two girls.
In an e-mail to Chavan, Katju warned of "legal consequences" if he failed to take action against the police personnel concerned.