Opposition groups initially demonstrated against high prices for commodities, but are increasingly demanding political reform, The Wall Street Journal said.
Government officials have promised some concessions, including the lifting of Algeria's long-time state of emergency. So far, Algeria has avoided the violent clashes that left protesters dead in Egypt, Yemen, Bahrain and Libya.
The protests were organized by the opposition groups Rally for Culture and Democracy and the Algerian League for the Defense of Human Rights.
Rally for Culture and Democracy spokesman Hacene Mezoued said some protesters were sandwiched between the police and pro-government demonstrators.
The newspaper said it was unable to get a comment from government officials or police.
Notable deaths of 2014 [PHOTOS]