Protesters blew whistles and waved flags in Istanbul's Taksim Square, the epicentre of the protests which erupted on May 31.
Fresh rallies were also held in the capital Ankara, with over a thousand people gathering peacefully in the central Kizilay Square, singing revolutionary songs and dancing.
Erdogan, meanwhile, was meeting in Istanbul with top officials of his Justice and Development Party (AKP) to discuss the crisis.
Turkey's assertive leader on Friday called for an immediate end to the protests, saying his government was open to "democratic demands" but insisting that the protests were "bordering on vandalism".
The political turmoil erupted after police cracked down heavily on a small campaign to save Gezi Park from demolition, spiralling into nationwide protests against Erdogan.
Police have used tear gas and water cannon to disperse demonstrators in clashes that have left three dead and thousands injured.
In a bid to calm tensions, Istanbul's mayor Kadir Topbas on Saturday said the park would not be turned into a shopping mall, as some feared.
The national doctors' union says the civil unrest has so far left two protesters and a policeman dead while almost 4,800 people have been injured across Turkey.