The bench of Justice Naima Haider and Justice Razik-Al-Jalil passed the order after an appeal hearing in a contempt of court case.
The HC asked the authorities to provide details on the measures by four weeks and fixed April 25 for the next hearing.
Earlier on August 25, 2010, the High Court issued the directive after hearing a writ petition filed by Human Rights and Peace for Bangladesh (HRPB) to secure the sanctity of the Shaheed Minar, which was built to commemorate those killed during the Language Movement of 1952.
The HC directive asked for several regulations including on security measures around the national monument and restriction of rallies on the main altar of the Shaheed Minar.
Advocate Manzil Murshid of HRPB said the appeal was filed as the old HC directives are yet to be implemented completely.