The oil-rich Central Asian nation was shaken this month by the worst bout of violence in its post-Soviet history during which at least 225 people were killed, most of them in Almaty.
On Wednesday, a group led by Mukhtar Ablyazov, a former Kazakh banker turned government critic in exile, said it would hold protests outside local government buildings in major cities throughout the country of 19 million.
A Kazakh court has ruled Ablyazov's political movement, Democratic Choice of Kazakhstan, was extremist.
Police in Almaty said they were carrying out an "anti-terrorist operation".