Justice M. Enayetur Rahim and Justice Md. Mostafizur Rahman accepted their appeals for hearing on Sunday.
The HC also stayed the part of the trial court verdict that fined the convicts of the cases. Besides, the court asked the trial court concerned to submit the records of the cases before the High Court.
Assistant Attorney General Yousuf Mahmud Morshed, who stood for the state in the court, said that 44 convicts including former State Minister for Home Lutfozzaman Babar and former Deputy Minister for Education Abdus Salam Pintu filed appeal for hearing through the jail authority.
However, the convicts who are absconding will not get any scope to file appeal for hearing, he added.
Earlier, a speedy trial tribunal sentenced 19 people, including Lutfozzaman Babar and Abdus Salam Pintu, to death while 19 others, including BNP acting Chairman Tarique Rahman, to life imprisonment on October 10 last in two cases filed over the August 21 grenade attack.
On August 21, 2004, at least 24 people were killed and around 300 injured in the grisly attack on an Awami League rally on the capital's Bangabandhu Avenue.