Several people were hurt.
Police wielding batons and shields stopped demonstrators from leaving the headquarters of a democratic opposition party that called the Saturday march to the National Assembly in Algiers.
Some demonstrators waved Tunisian flags — a nod to the street unrest.
Algeria's government in 2002 enacted law banning public gatherings — a move largely targeting militants involved in a bloody insurgency that erupted in the country a decade earlier.
"There are several injured... and numerous arrests," Said Sadi, the head of the opposition Rally for Culture and Democracy (RCD) said.
Seven police officers were also hurt in the clashes, officials said. Two of the police are in a serious condition, a police source told the official APS news agency.
Five people were arrested, APS said, also citing a police source.
The government had warned people not to show support for the demonstration in central Algiers in a statement issued on the eve of the march, amid fears of popular unrest spreading from neighboring Tunisia.
Among those arrested was the head of the party's parliamentary group, Othmane Amazouz, the RCD leader said.
Another of the party's MPs, Arezki Aiter, was detained but released after an hour, the party said.
Around 300 people had gathered for the rally, intending to march from the city's Place de la Concorde to the Parliament building, but they were quickly blockaded by riot police armed with batons and tear gas, which prevented the group from moving for six hours.
Sadi said his party's headquarters in the city's main avenue had been put under siege by police, describing himself as "a prisoner.”
"We cannot wage a peaceful campaign when we are under siege," he said, using a megaphone to address the crowd from a first-floor window.
The protesters in the street below waved Tunisian as well as Algerian flags and shouted "A free Algeria, a democratic Algeria" in Arabic, and "Murder State.”
A journalist saw one of the party's regional leaders, Reda Boudraa, bleeding from the head after being hit by a police baton. Boudraa was taken away in an ambulance with another injured protester.
Several people were arrested, most of them youths. One was dragged away by six men in civilian clothes and beaten in the doorway of a nearby building.
The government warning, carried by official news agency APS, stated: "Citizens are asked to show wisdom and vigilance and not respond to possible provocation aimed at disturbing their tranquillity, peace of mind and serenity." "Marches are not allowed in Algiers" the statement warned, adding that "all assemblies on public roads are considered a breach of public order.”
Mounting public grievances over unemployment and rising costs sparked protests in Algeria earlier this month which left five people dead and more than 800 injured.
The government responded swiftly by reducing the prices of oil, sugar and other basic necessities, which had risen sharply, while buying up a million tons of wheat amid assurances that subsidies on essential goods like flour would continue.
Unrest still simmers, however, and within the past two weeks eight people set themselves on fire in Algeria, although some cases were deemed to be linked to mental health issues.
Students at the Mouloud-Mammeri University at Tizi-Ouzou in the restive Kabylie region east of Algiers had said that they would back the protest.
In a statement the student leadership praised the Tunisian uprising and said it "inspired and motivated all the patriots of North Africa." Algerian commentators have said that more Tunisia-style protests could break out in Algeria, a country with similar social problems.
Unemployment, specifically of the young, is a key issue in Algeria, a country where according to the authorities 15 million of the 36 million population is under the age of 30.
