"If I've hurt anyone's sentiments, I fold my hands and apologize to everyone," Mr Sharda, 40, said after his arrest.
A spokesperson for the Dera Sacha Sauda, the sect headed by Mr Singh, said saying sorry wasn't enough. "Anyone can commit a crime and then apologize," said the spokesperson, Aditya Insan, defending the sect's decision to file a police case against Mr Sharda.
He described Mr Sharda's portrayal of the Dera chief as derogatory and offensive and said it had hurt the religious sensitivities of lakhs of his followers.
Earlier this evening, however, Mr Singh, 48, tweeted the apology was accepted.
Mr Singh is often called The Guru of Bling because of his bejewelled costumes and flashy appearances on motorcycles. The sect he heads, headquartered in Haryana, claims nearly 50 million followers. Mr Singh has appeared in two films in the lead role.
I was busy shooting OnlineGurukul; just got to know, devotees are hurt due to Kiku's action.If he has apologized, no complaint from my sideGURMEET RAM RAHIM (@Gurmeetramrahim) January 13, 2016
Two years ago, the CBI was ordered by a court to investigate claims that Mr Singh forced 400 followers to undergo castrations at his ashram, in order to "experience God".