Hundreds of riot police backed up by water cannon trucks moved in on several thousand protesters chanting for Erdogan's dismissal.
"This is but a start, the battle continues!" the protesters yelled, throwing red carnations. "It is by resisting that we will prevail!"
The protesters had gathered a week after police evicted thousands of people from the adjacent Gezi Park, the epicentre of nationwide demonstrations that had shaken Turkey for much of June and presented Erdogan and his Islamic-rooted government with the biggest challenge of their decade-long rule.
"The people and the AKP (ruling Justice and Development Party) government have foiled the plot... Hatched by traitors and their foreign accomplices," Erdogan said on Tuesday.
Confident he has weathered the storm, he warned against any resurgence of the protests.
"From now on, there will be no question of showing any tolerance to people or organisations who engage in violent acts."
The crisis began when a small campaign to save Gezi Park's 600 trees from being razed in a redevelopment project was met with a brutal police response on May 31.
Four people have been killed and nearly 8,000 injured in the turmoil, according to the Turkish Medical Association.
Hundreds have also been arrested across the country in connection with the demonstrations and at least 46 people have been charged, most of them accused of belonging to "terrorist" groups and destruction of property, according to lawyers groups.