"Twenty-four hours have elapsed since the incident and she should immediately apologise or we will launch a protest," said SN Garg, secretary of the Teerth Purohit Sangh Trust, the organisation of priests of the temple.
"The priests of the temple were furious over the incident and have lodged a protest against it with the trust," he said.
"In view of the volatile situation and the resentment of the priests, the star and her mother left the temple," said the Trust's president Lado Ram Sharma, referring to Aishwarya's visit to the shrine on Thursday.
The trust will organise special prayers called shanti paath and sadbuddhi yajna on Saturday at the Pushkar lake so that Aishwarya gets the "wisdom" to offer an apology, said S N Garg, secretary of the Teerth Purohit Sangh Trust.
Reports said one of three bodyguards who accompanied Aishwarya to the temple was inebriated. The bodyguards pushed back people who rushed to have a glimpse of the star, the reports said.
Sharma said the Trust convened an emergency meeting to discuss the incident. The Trust's officials said local people and priests were keen on avoiding controversies as they could have a negative impact on people visiting the shrine.
Ajmer's Superintendent of Police Sunil Mathur said that police had no prior information about Aishwarya's visit to Pushkar and that no complaint has been filed against her bodyguards.
Aishwarya, accompanied by her mother, visited the tomb of Sufi saint Khwaja Moinudeen Chisti and offered prayers at the Brahma temple on Thursday.