The protest was scheduled to take place just over a week after a wave of demonstrations in neighbouring Tunisia forced that country's long-standing president to flee, sending shockwaves through the Arab world.
The head of the RCD party, the biggest opposition group in Algeria's parliament, said party officials were surrounded by riot police when they tried to leave their headquarters building to go to the planned protest.
"We have 32 injured, including a member of parliament," party chief Said Saadi told Reuters by telephone. "We have been prevented from marching by an impressive security apparatus. More than 1,500 (police) were on the streets of Algiers."
After the clash with police, a small group of RCD supporters remained outside the party headquarters chanting "The authorities are assassins!" and "A free and democratic Algeria!"
Algeria's official APS news agency quoted a police source as saying arrests had been made and that seven police officers had been injured, two of them seriously.
Authorities in Algeria, a major exporter of energy, had earlier refused permission for the protest, saying it would disturb public order. They had urged members of the public to "ignore [...] provocative acts."
At the planned venue for the protest, on May 1 Square near the centre of Algiers, only about 15 protesters showed up, a Reuters reporter at the scene said.
Nevertheless, several hundred police in full riot gear were on standby in vehicles nearby, and a police helicopter hovered over the centre of the city.
Algeria's opposition says the state is failing to invest energy revenues in improving peoples' standard of living, that it imposes restrictions on political parties and that the army is too powerful.
A former French colony which supplies about 20% of Europe's gas supplies, Algeria is still emerging from a conflict between security forces and Islamist militants which killed an estimated 200,000 people.
What role for Islamists?
Analysts say that the downfall of Ben Ali's police state (see 'Background') may leave Tunisia open to infiltration by extremists from neighbouring Algeria, where war between authorities and Islamists has killed 200,000 people in the last two decades.
"The Islamist movement was the most oppressed of all the opposition movements under Ben Ali. Its followers are also much greater in number than those of the secular opposition," said Salah Jourchi, a Tunisian expert on Islamic movements.
Secularism has been strictly enforced in Tunisia since before its independence from France in 1956. Habib Bourguiba, the independence leader and long-time president, was a nationalist who considered Islam a threat to the state.
(EurActiv with Reuters.)