Police early Wednesday used tear gas and water cannon on hundreds of protesters, who ignored warnings to disperse in Istanbul, Ankara and the southeastern city of Hatay, where a young protester died a day earlier.
The violence came after a second major trade union confederation announced it would join protests against the government, calling a strike for Wednesday.
In the western city of Izmir, police detained at least 25 people early Wednesday for tweeting "misleading and libelous information", state-run Anatolia news agency reported.
On Tuesday, Deputy Prime Minister Bulent Arinc apologized to legitimate demonstrators injured by the security forces, a gesture welcomed by the United States.
But that did not appease outraged protestors.
Thousands gathered at Istanbul's Taksim Square for a sixth day Wednesday, yelling defiance at Erdogan, who earlier had dismissed the protesters as "extremists" and "vandals."
He was in Algeria on the second day of a four-day official visit to north Africa.
"The vandals are here! Where is Tayyip?" yelled the crowd.
They accuse Erdogan, who has won three successive national elections, of imposing conservative reforms on the predominantly Muslim but constitutionally secular nation.
The wave of protests broke out on Friday after police tear-gassed demonstrators at a peaceful rally against plans to build on an Istanbul park.
On Tuesday, Arinc said sorry to those who had been caught up in that initial violence.
"I apologize to those who were subject to violence because of their sensitivity for the environment," he said, though he added that his apology excluded "the rioters."
"The government has learnt its lesson from what happened," he added. "We do not have the right and cannot afford to ignore people. Democracies cannot exist without opposition."
He called on "responsible citizens" to stop the protests.
Two people have been killed in the clashes, officials and medics say, and rights groups say thousands have been injured. The government puts the figure at around 300.
Erdogan, whose Justice and Development Party (AKP) first took power in 2002, has accused the main opposition Republican People's Party of having a hand in the protests.