Prime Minister Tayyip Erdogan has agreed to meet on Wednesday with leaders of the movement whose peaceful protests in Istanbul spiraled into a wave of anti-government demonstrations across Turkey.
Erdogan has repeatedly dismissed the protesters as "capulcular", or riff-raff. But Deputy Prime Minister Bulent Arinc said on Monday leaders of the Gezi Park Platform group had asked to meet him in an effort to end unrest in which police have blasted demonstrators with tear gas and water cannon.
"They asked to meet the prime minister and he agreed to meet with the organizers," Arinc told reporters in Ankara.
The group takes its name from a park in a corner of Istanbul's Taksim Square. A campaign against government plans to develop the park in turned into a show of defiance against Erdogan and the ruling AK Party.
The protests have shaken the predominantly Muslim country's image as a stable democracy in a turbulent region and as a vibrant emerging market for investors. Three people have been killed and about 5,000 hurt.
The violent police action has drawn criticism from the West and Erdogan has increasingly accused foreign forces of trying to aggravate the troubles.
A core of protesters on Monday showed little sign of easing their occupation of Taksim Square after Erdogan warned his patience may run out.
Many are camped out in tents and they control a large area around the square, with approach roads barricaded by masonry, paving stones and steel rods. Police have withdrawn completely from the area, water cannon kept hundreds of meters away by the side of the Bosphorus waterway.
"We want life on the square to return to normal," said Eyup Muhcu, head of the Chamber of Architects and part of the Taksim Solidarity Platform. "We are ready for dialogue...but the prime minister's remarks indicate he is not open to dialogue," he said, speaking before the Wednesday meeting was announced.
In a move that might add to discontent among secular Turks, President Abdullah Gul approved a bill that scales back the sale and consumption of alcohol.
Turkey has a secular constitution but the Islamist-rooted AK party has come under fire for undermining the separation of state and religion. Critics accuse Erdogan and the party of trying to interfere in their lives.
The bill, passed by parliament last month, bans alcohol producers from sponsoring events and venues where alcohol is sold and consumed. It also prohibits the public display of alcoholic drinks and requires health warnings on packaging.
Erdogan also criticized speculators after the stock market fell almost 15 percent last week.
"Those who attempt to sink the bourse, you will collapse... If we catch your speculation, we will choke you. No matter who you are, we will choke you," he said.
Timothy Ash, head of emerging markets at Standard Bank, said his comments marked an about-turn for an administration that valued foreign investment and had been sensitive to markets.
"That era now seems to have ended and the administration appears set on a collision course with foreign investors and with markets," Ash said.
Ratings agency Moody's said prolonged uncertainty could hit tourism revenues and slow investment in Turkey's capital markets.
The cost of insuring Turkish debt against default rose to the highest since the end of October 2012 on Monday, according to data from Markit, although it remained far from crisis level. Stocks fell further and the lira weakened.