The petition, which was filed in September, has appealed to the court to allow worship on the spot again.
The petitioner's advocate, Yogesh Siroja, said civil judge Manmohan Chandel has ordered notices to the Ajmer Dargah Committee, the Ministry of Minority Affairs and Archaeological Survey of India (ASI) office in New Delhi seeking their response.
This comes after similar claims were made for key shrines across the country, including the ones in Varanasi, Mathura, and the Bhojshala in Dhar.
The Ajmer court's order follows violence in Sambhal, Uttar Pradesh, where four persons died and many were injured after a clash was triggered by a local court's order for a survey at a mosque.
The petitioners had told the court that the mosque was built after destroying an old temple.