They also demand that an end be put to attacks on opposition supporters in the run-up to the 6 November parliamentary elections.
The protesters belong to Yeni Fikir (New Thinking), a youth movement close to the reformist wing of the Popular Front Party of Azerbaijan (AXCP).
Yeni Fikir Chairman Ruslan Basirli was arrested earlier this month on charges of receiving foreign money in return for a promise to topple the government of President Ilham Aliyev. His arrest sparked a wave of violent anti-AXCP protests throughout the country.
(Turan/day.az/Zerkalo.az/ekho.az/AP)