The party had given no hint of its planned course of action, but the embargo was scheduled to disappear earlier on Friday.
Islam, 26, the deputy coordinator of Individuals Against Discrimination, told AFP from his hospital bed on Monday that he feared for his career.
He claimed that two weeks prior, a group of people acting as officers detectives carried him to an undisclosed location while blindfolded and handcuffed him.
Islam continued, claiming that he had awakened the following day on a Dhaka roads.
Mahmud previously told AFP that during the height of the upheaval last week, he had also been detained by police and subjected to beating.
Three senior police officers in Dhaka all denied that the group had been taken from the doctor and taken into custody on Friday.
THOUSANDS OF Detention
Since the unrest started last month, authorities have made at least 4, 000 arrests, including 2,500 in Dhaka, according to a statement released on Thursday.
Following the restoration of a system that reserved more than half of government positions for specific candidates in June, student protests started this month.
According to government figures, around 18 million fresh Bangladeshis are without jobs, which greatly upset graduates who are in a severe jobs crisis.