The 30-member panel has also asked producers of the movie and officials of the information and broadcasting ministry to appear before it and brief about the controversy relating to the Rs 150 crore film.
"The panel has asked Mr Bhansali and Mr Joshi to appear before it and present their views on the movie. They can present their case before the panel. The members have also decided to call the producers of the movie," chairman of the panel Anurag Thakur told PTI.
The committee is scheduled to meet on Thursday.
Actors Paresh Rawal and Raj Babbar, who are members of Parliament, are also part of the panel which will examine the issues relating to the movie.
Parliamentary sources said they have reached out to Mr Bhansali, but he appeared to be "shying away" from appearing before the panel.
The censor board is yet to clear the film.
The film, starring Deepika Padukone, Shahid Kapoor and Ranveer Singh, is based on Rajput queen Padmini.
As allegations of distorting history in the film triggered protests in various states, the makers of the movie has deferred its release date.
The film was scheduled to release on December 1, this year.
The Karni Sena, a fringe group, as well as the BJP have been critical of the film and a number of BJP ruled states have already banned it.
Another parliamentary panel has also called the officials of the ministry and censor board over the controversy.