The body of the 19-year-old girl was found in Jalesar area of the district on April 24.
The leaders have claimed that the four youths have been falsely implicated in the case.
Former MLA Pratyendra Pal Singh Pappoo, former MLA Kuber Singh Agaria and Zila Panchayat member Ram Kishan Yadav along with leaders of various social organisations threatened to launch a movement in the entire district if the accusation against the four youths was not withdrawn.
The matter is being investigated, police said.