In a statement issued on October 4, the agency expressed concern over the "restrictive environment" activists currently face in Azerbaijan.
The statement said all demonstrations complying with international human rights standards should be allowed.
It added that the authorities should not use excessive force or administrative measures against peaceful demonstrators, and should not undermine freedom of expression, opinion, and assembly.
Azerbaijan has been widely criticized for cracking down on dissent, independent media, and activists.
Also on October 4, several independent journalists were beaten during an opposition election rally in the central town of Sabirabad.
The opposition's single candidate, Camil Hasanli, is seeking to unseat the incumbent, Ilham Aliyev.