The bench of Justice M Enayetur Rahim and Justice Ashish Ranjan Das issued the rule on Wednesday after initial hearing of a writ petition filed by Nazmul Haque Prodhan, the general secretary of the other JaSoD faction.
The chief election commissioner, the Election Commission secretary and Inu have been given four weeks to respond to the rule.
Lawyers Shahdeen Malik and Zahirul Alam Babar argued for the petitioner while Deputy Attorney General Tapas Kumar Biswas stood for the State.
JaSoD experienced the last split during its national council on Mar 12 over Inu's decision to make Shirin Akhter general secretary.
Leaders Moin Uddin Khan Badal, Sharif Nurul Ambia and Prodhan, and their followers formed another committee besides the Inu-Shirin panel.
Prodhan on May 12 filed a petition at the EC to review its decision. He later moved the High Court as the EC did not settle the petition.
On June 22, the High Court ordered the EC to dispose of the review petition. The commission upheld its previous decision in an announcement on Aug 10.
Prodhan on Sep 26 filed a writ petition challenging the EC's decision.
After the High Court issued the rule, Babar told reporters that the EC did not call the Badal-Ambia faction to the hearing of the review petition.
"It was unlawful and that's why we filed the writ petition."