The writ petition, filed in the morning, sought payment of Tk 10 lakh within 15 days.
It also sought directives to formulate a separate law to try people involved in mob-beating and a ruling on why the defendants’ failure to save Renu should not be declared illegal.
Besides, the writ, filed by Supreme Court Lawyer Ishrat Hasan, seeks directive to erase all rumour-related posts from Facebook.
The bench of Justice Moinul Islam Chowdhury and Justice Md Ashraful Kamal is scheduled to hear the petition later in the day.
Secretaries to the Cabinet, home, law and information, and the police chief, Dhaka Metropolitan Police commissioner and officer-in-charge of Badda Police Station have been made defendants.
Renu was beaten to death over child abduction rumour at North Badda in the city on July 20.
Her family said she had gone to the area to look for a suitable school for her children. A video of the incident went viral on Facebook, triggering widespread outrage.
Thirteen suspects have so far been arrested in a case filed over the lynching.