The National Alliance to Support Legitimacy called on Friday for nationwide protests against “the disappearance of justice and the annulment of law and the judiciary".
The group, which supports ousted president Mohamed Morsi, has organised protests on an almost weekly basis since his ouster last summer, although numbers of protests remain small after police crackdowns on public demonstrations.
In a statement, the group also criticised the speech given by President Abdel-Fattah El-Sisi at the UN Gneral Assembly this week, describing it as a "failure."
"The premature speech of the second Mubarak is an expression of an exposed state of denial attempting to conceal the obvious truth and mislead international public opinion of his crimes," the statement read.
El-Sisi has stressed during his speech that mass protests against Morsi on 30 June 2013 revealed Egyptians’ political will and marked a second revolution.
Morsi’s Muslim Brotherhood and its allies have refused to recognise the legitimacy of the post-Morsi authorities.
Public protests are illegal in Egypt unless given prior permission from the police, under the terms of a controversial law issued last year which has seen thousands of protesters jailed.