Backed by armoured vehicles, police wearing white helmets and carrying shields massed in areas around the square, but there were no clashes between them and protesters in the nearby park.
On Monday night, the Turkish riot police flooded Tunali Hilmi street in the capital Ankara which has not largely experienced demonstrations until now.
On the third consecutive night of clashes between protesters and police, most of the demonstrators escaped after they were charged by the police and the restaurant owners shut their restaurants to avoid the gas.
The new wave of protests came despite the fact that Erdogan had accepted to meet protest leaders earlier in the day.
On Monday, Deputy Prime Minister Bulent Arinc said Erdogan would meet the protest leaders on Wednesday, but did not say exactly who would be invited to the meeting.
For the past 11 days, tens of thousands of anti-government protesters have held demonstrations in Istanbul, Ankara, Izmir, Mugla, Antalya, and many other cities and towns.
Two protesters and a policeman have been killed and almost 4,800 people have been injured in the unrest, according to the Turkish Human Rights Association.
Erdogan has been harshly criticized for the way he has handled the crisis, and Amnesty International has censured the Turkish police for using excessive force against peaceful protesters.
The anti-government protests began on May 31 after police broke up a sit-in staged in Istanbul’s Taksim Square to protest against the demolition of Gezi Park.
The protesters say Gezi Park, which is a traditional gathering point for rallies and demonstrations as well as a popular tourist destination, is Istanbul's last green public space.