Hundreds of police in helmets and shields blocked access to two central squares where protestors on Feb 12 and 19 tried to stage marches, which have been banned in the capital since 2001.
The demonstration against President Abdelaziz Bouteflika's decades-old regime was set to start two days after the government lifted a state of emergency in force for 19 years, amidst a split in the Algerian opposition.
Police were backed up by armoured vehicles as a helicopter flew overhead, but witnesses said their overall presence was less than for both earlier rallies this month.
Last weekend, protesters clashed with riot police who stopped a bid by some 3,000 people to march in the capital.
On Thursday, the 73-year-old Bouteflika also promised to place "anti-corruption" at the heart of government action, after unprecedented protests were staged in January that left five dead.
The measures were seen as conciliatory efforts to appease public anger after anti-government protests sweeping much of the Arab world brought down the leaders in neighbouring Tunisia and in Egypt.
The new protest was called after a split in the opposition this week. The Rally for Culture and Democracy (RCD) vowed it would march Saturday "and every Saturday".
Its former ally, however, the National Coordination for Change and Democracy (CNCD), an opposition umbrella group formed last month, begged out, saying Friday it planned to "revamp the movement".
The CNCD has said it wants the immediate end of Bouteflika's regime, citing the same problems of high unemployment, housing and soaring costs that inspired the uprisings in Tunisia and Egypt.