Algerian opposition groups have said they will follow up the protests held this weekend by calling a demonstration in Algiers, the capital, every Saturday until the government is changed.
"We will continue to march until the regime steps down. Each Saturday we will maintain the pressure," said Mohsen Belabes, a spokesman for the RCD opposition party which helped organised the demonstrations.
Elias Filali, an Algerian blogger and activist, quoted Ali Yahia Abdennour, a senior figure and human right activist, as saying: "We should continue protesting every Saturday in the same square, we will gather momentum as we progress we want our dignity back.
"Yesterday the police has brutally beaten many protesters amongst them a pregnant women, old ladies, a journalist, young men and women, we should carry on protesting until we get our rights."
The call came as hundreds of stone-throwing demonstrators clashed with police on Sunday in the eastern city of Annaba.
Four police officers were slightly injured during clashes with young protesters outside the local government headquarters.
Several thousands protesters, inspired by revolts which overthrew entrenched leaders in Egypt and Tunisia, defied a police ban and protested in Algiers on Saturday.
Widespread discontent with unemployment, poor housing conditions and high food prices sparked rioting in early January across the country.
Local media reported that Abdelaziz Bouteflika, the president, is preparing to make wholesale changes in his government line-up, a move which could relieve some of the pressure on his administration.
"What happened in Tunisia and Egypt is not likely to happen here," said Nacer Jabi, an Algerian sociologist, as he watched the protest on Saturday.
"This march shows ... that the [political] parties are unable to mobilise the crowds."
The resignation on Friday of Hosni Mubarak, Egyptian president, and last month's overthrow of Tunisia's leader, have led many to ask which country could be next in the Arab world, with its flammable mix of authoritarian rule and popular anger.
Widespread unrest in Algeria could have implications for the world economy because it is a major oil and gas exporter, but many analysts say an Egypt-style revolt is unlikely as the government can use its energy wealth to placate most grievances.
The government has said it refused permission for Saturday's rally for public order reasons, not because it is trying to stifle dissent.
It has said it is working hard to create jobs, build new homes and improve public services.
Other countries have also felt the ripples from the revolts in Egypt and Tunisia.
Jordan's King Abdullah replaced his prime minister after protests, while in Yemen, Ali Abdullah Saleh told opponents he would not seek a new term as president.
The Bahraini government has also made several concessions in recent weeks, including promising higher social spending.
Activists there have called for protests on February 14, the anniversary of the country's 2002 constitution.
There have also been calls for an anti-government rally in Iran on Monday.