A heavy security presence contained the protest in Algiers then broke it up Anti-government rallies in the capitals of Algeria and Yemen, inspired by events in Egypt, have been broken up.
Riot police in Algiers dispersed thousands of people who had defied a government ban to demand that President Abdelaziz Bouteflika step down.
A similar march in Yemen’s capital, Sanaa, calling for President Ali Abdullah Saleh to leave office was attacked by government supporters.
Egypt’s Hosni Mubarak stepped down on Friday after 18 days of mass protests.
Both Yemen and Algeria, like other countries in the region, have recently witnessed demonstrations for greater freedoms and improved living standards.
Protesters in Algiers evaded thousands of police who were deployed in and around the capital city ahead of the demonstration.
Public demonstrations are banned in Algeria under a state of emergency in place since 1992.
Anti-government protesters took to the streets of Yemen
The protesters gathered at Algiers’ 1 May Square on Saturday morning.
They chanted “Bouteflika out!” – in reference to the country’s president, who came to power in 1999.
The heavy police presence prevented them from marching to Martyrs Square, about 5km (3 miles) away. Rights groups said hundreds of people were arrested.
By late in the afternoon only a few hundred people were left in 1 May Square.
But the protest’s organisers hailed it as a success.
“We’ve broken the wall of fear, this is only a beginning,” said Fodil Boumala, one of the founders of the National Co-ordination for Change and Democracy.
“The Algerians have won back their capital.”
In Yemen, it was supporters of President Saleh, who has been in power since 1978, who forced anti-government protesters from the centre of Sanaa.
Several thousand protesters had gathered chanting: “After Mubarak, it’s Ali’s turn.”
Supporters of the president, armed with traditional Yemeni knives and sticks, turned up and forced the protesters, many of them students, to flee.
It came after protesters celebrating the toppling of Egypt’s President Mubarak on Friday night were driven out from Sanaa’s Tahrir Square by armed men.
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