The High Court on May 5, in a suo moto rule, directed the government to engage CID into the investigation along with Detective Branch (DB) of police in the cases.
In another order on July 9, the HC said the CID will conduct the inquiry but not investigate the incident.
Against the two HC orders, Attorney General Office filed two separate appeals on May 11 and October 31 with the SC seeking an exemption on the CID from probing.
The government in the appeals said that two (Detective Branch of police and CID) cannot hold investigations in same criminal cases simultaneously.
DB has been conducting the investigation of the cases from the very beginning.
Meanwhile, Deputy Attorney General AFM Najmul Haque told The Daily Star that Rapid Action Battalion, inspector general of police and the government-formed seven-member committee are likely to submit progress reports on their investigations in the cases before the HC on Thursday.
On April 27, seven people including Narayanganj city panel mayor Nazrul Islam and senior lawyer Chandan Sarkar were abducted from Siddhirganj of Narayanganj city.
Later on April 30, six bodies of them were spotted floating in the Shitalakkhya river. The seventh surfaced the next day.