"I will not eat anything till the time Asaram is arrested," the victim's father told reporters.
He had earlier announced he would stage a fast-unto-death if the godman was not arrested by August 30.
On the occasion, the protesters handed over a memorandum addressed to the President of India and Governor of Uttar Pradesh to the district magistrate, containing the demand for arrest and strong punishment for Asaram, who has been evading police.
The district authorities have made elaborate security arrangements at the Collectorate and are not allowing the entry of people inside the premises, an official said.
Meanwhile, security around the Chandapur ashram of Asaram has also been stepped up with heavy deployment of police force, the official added.
72-year-old Asaram has been booked for allegedly sexually assaulting the teenage girl in a Jodhpur ashram.