Taksim Solidarity, which combines an array of political groups, had called a march to enter the sealed off Gezi park, but the governor of Istanbul warned that any such gathering would be confronted by the police.
"We are going to our park to open its doors to its real owners ... We are here and we will stay here ... We have not given up our demands," the umbrella group said in a statement.
On Saturday, police in riot gear chased protesters into side streets in what appeared to be the biggest police intervention since the mid-June protests that saw Taksim Square sealed off by makeshift barricades.
"They can use Gezi Park as they wish, without gathering or demonstrating there ... If there is an illegal demonstration or march, of course we will intervene by using water cannons," Interior Minister Muammer Guler said.
Protesters in Istanbul chanted "Together against fascism" and "Everywhere is resistance".
Witnesses said that police detained dozens of protesters, but later in the evening many still remained in side streets in the Taksim area, including youths and women, some in gas masks.
"We are here today to claim our park back. It was supposed to be open tonight. They (authorities) called us occupiers, but the park has been occupied by the state for weeks now," said 41-year-old web designer Asim Elci.
A police crackdown on a group protesting against the planned redevelopment of Gezi Park, a leafy corner of Taksim, triggered nationwide protests last month against Erdogan, accused by critics of increasingly authoritarian rule after a decade in power.
In the capital, Ankara, hundreds of protesters also held a similar rally.