Police 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.
"You are being unfair to us, that is enough!" one protester was seen yelling at the police after warnings to quit an area close to Erdogan's Istanbul office.
Erdogan's government earlier won praise from the United States for apologising to injured protesters, but that concession did not appear to have stemmed popular anger.
"The vandals are here! Where is Tayyip?" yelled the crowd.
More From This Section
They accuse Erdogan, who has won three successive national elections, of imposing conservative Islamic reforms on the predominantly Muslim but constitutionally secular nation.
"If they step back, if they change something in Turkey, the conservatism and the things they've done, then maybe the crowd can go home," said Didem Kul, a 24-year-old student in Taksim Square.
Even fans from rival football teams Galatasaray, Besiktas and Fenerbahce linked arms, united in protest.
Earlier today, Deputy Prime Minister Bulent Arinc apologised to protesters who had been injured when the clashes erupted last week. 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.
"I apologise 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".
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.