Their defiant statement came despite PM Recep Tayyip Erdogan’s promise to halt a redevelopment plan which sparked two weeks of anti-government unrest.
Recep Tayyip Erdogan’s offer was presented as a major concession.
But after all-night discussions in Gezi Park, the protesters said their movement was bigger than a simple conservation protest.
“We will continue our resistance in the face of any injustice and unfairness taking place in our country,” the Taksim Solidarity group, seen as most representative of the protesters, said.
“This is only the beginning.”
Meanwhile, in the capital Ankara, riot police again deployed tear gas and water cannon to disperse demonstrators overnight. About 30 protesters were reported to have been arrested.
Later on Saturday, supporters of Recep Tayyip Erdogan’s ruling Justice and Development Party (AKP) are expected to take to the streets of the capital for an election rally to show support for the embattled premier.
The prime minister’s offer to stop the Gezi Park redevelopment until a court ruled on its legality was his first conciliatory gesture since the challenge to his Islamist-backed government began.
He had previously taken a tough line on the protests, branding the demonstrators “extremists” and “looters”. He said the unrest was being encouraged by foreign forces to undermine Turkey and its economy.
“Young people, you have remained there long enough and delivered your message…. Why are you staying?” Recep Tayyip Erdogan said in a speech broadcast live on television in which he made his offer.
The contested Gezi Park is a rare patch of green in Turkey’s biggest city.
Last month, an Istanbul court issued an initial injunction against the plan to cut down trees in the park to make way for a shopping centre and replica 18th-Century military barracks. The government has appealed against the ruling.
The project was the initial spark for the protests, which then broadened into anti-government demonstrations in several cities which saw violent clashes between police and demonstrators.
Five people have died and thousands have been injured since the protests began on 31 May, spreading to the adjacent Taksim Square a day later and then to other towns and cities across Turkey.
Protesters have accused Recep Tayyip Erdogan’s government of becoming increasingly authoritarian and of trying to impose conservative Islamic values on a secular state.
The police crackdown on protesters in Istanbul, Ankara, and other towns and cities has drawn international concern, especially from Europe.
And Turkish broadcasters have been heavily criticized for not covering the protests in their early days.
The BBC has suspended its partnership with Turkish broadcaster NTV following its decision not to transmit the BBC programme Dunya Gundemi (World Agenda).
The dropping of the programme came after NTV had apologized to its staff and viewers for not covering the protests when they first began.
Turkey protest timeline:
May 31: Protests begin in Gezi Park over plans to redevelop one of Istanbul’s few green spaces
June 3: Protesters establish camps with makeshift facilities from libraries to food centres
June 4-10: Protests widen into show of anti-government dissent in towns and cities across Turkey; clashes between police and demonstrators
June 11-12: Night of clashes see riot police disperse anti-government demonstrators in Taksim Square, which adjoins Gezi Park; camps in the park remain
June 13: PM Recep Tayyip Erdogan issues a “final warning” to protesters to leave Gezi Park
June 14: Government agrees to suspend Gezi Park redevelopment plans until a court rules on the issue, PM holds talks with members of a key protest group
June 15: Protesters vow to continue occupying Gezi Park
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