Pooja Ben, a close disciple of Asaram Bapu, had come to the family's house and pleaded with them to end the matter, the father of the girl said in Shahjahanpur, Uttar Pradesh.
When contacted by IANS, a spokesperson of Asaram Bapu's ashram in Indore said she had no knowledge of the matter.
The girl had last week alleged that Asaram Bapu had raped her during one of her stays at the seer's ashram.
A case has been filed by Rajasthan Police and Asaram Bapu has been served summons to present himself Aug 30. However, citing prior engagements till Aug 31, Asaram Bapu has sought more time to appear before police.
The seer has refuted all charges.
"She (Pooja Ben) came to our house, touched the feet of my wife and requested her to withdraw the matter and also admitted that Asaram Bapu had committed a grave mistake," the father of the girl alleged.
He, however, said he would not do so at any cost as the seer (Asaram Bapu) had "played with their faith and emotions".
"We always held Bapu as god, and look what he has done," he said.
The girl's father criticised the seer for claiming that the allegations against him were false and part of a conspiracy.
"If he feels so, let there be a probe by the Central Bureau of Investigation (CBI), if I am found guilty of conspiracy, I should be hanged and he is found guilty, he should be sent to the gallows," the man said.
Security has been enhanced at the girl's house. An inspector, four constables and two women constables have been posted there. Legislator Suresh Kumar Khanna met the family Wednesday.