Huseyin Celik, deputy chairman of Turkey’s ruling AK party, says it is open to the idea of a referendum on controversial plans to redevelop Istanbul’s Gezi Park.
Huseyin Celik hoped the “gesture of goodwill” would clear the area.
But he warned: “Those… who seek to provoke and remain in the park will face the police.”
Police treatment of protesters campaigning against the redevelopment triggered broader demonstrations that have continued since May 31.
“We might put it to a referendum… In democracies only the will of the people counts,” Huseyin Celik said.
“We think that after this gesture of goodwill, people will decide to go home.”
Huseyin Celik’s comments represent the first time that the AK party has openly discussed letting voters decide what happens to the park. Demonstrators have remained there throughout the protests.
There has been a mixed reaction among protesters on Twitter, with some welcoming the proposal and others mistrustful of the authorities.
Turkish media reported on Wednesday that PM Recep Tayyip Erdogan had told the interior minister to end the protests in Gezi Park within 24 hours.
More than 20 opposition MPs have gone to the park to try to prevent any police intervention.
Senior European diplomats have expressed strong concern over Turkey’s response to the protests.
Hundreds of protesters have now gathered in Taksim Square, next to the park, although the square is about half as full as it was on Tuesday.
Police stood back along the edges of the square, which had been clear during the day after a series of violent clashes between police and protesters on Tuesday and overnight.
During the day, Recep Tayyip Erdogan met 11 activists, but protest leaders dismissed the meeting.
In both Istanbul and the capital, Ankara, on Wednesday thousands of lawyers left court in their black robes to march through the streets, protesting against the treatment of their colleagues during demonstrations.
Dozens of lawyers were briefly held in Istanbul on Tuesday as they voiced their opposition to police action to clear the square.
“Our friends who had been detained in Istanbul were taken under custody just because they were reading a press release,” said one of the lawyers in Ankara, Mehmet Toker.
“We are here to defend freedom of speech.”
Demonstrators accuse Recep Tayyip Erdogan of becoming increasingly authoritarian and trying to impose conservative Islamic values on a secular state.
“Oppression has been going on for months,” said another lawyer, Ege Inal.
“The government is exactly like the ones that they have been criticizing. That is why we are here.”
Late in the afternoon, Recep Tayyip Erdogan met a group of 11 people – including artists, architects and a social media specialist – to discuss the situation in Gezi Park.
But those in the park and Taksim Solidarity, an umbrella group seen as most representative of the protesters, said the activists did not speak for them.
“As police violence continues mercilessly… these meetings will in no way lead to a solution,” a statement from Taksim Solidarity said.
Recep Tayyip Erdogan had earlier said protests would no longer be tolerated, dismissing protesters as “looters”.
Turkish President Abdullah Gul, who has taken a more conciliatory line than PM Recep Tayyip Erdogan, said authorities should listen to protesters’ grievances.
“If people have objections, then to engage in a dialogue with these people, to hear out what they say is no doubt our duty,” he told reporters.
European Foreign Policy Chief Catherine Ashton said the unrest represented a “key moment” for Turkey, and a “chance for it to renew its commitment to European values”.
The Turkish Human Rights Foundation said more than 620 people had been injured in Tuesday’s police crackdown.
Since the protests began, four people have been killed, including one policeman and some 5,000 protesters as well as hundreds of police officers are estimated to have been injured.
Italian Foreign Minister Emma Bonino said the unrest was the “first serious test for the endurance of democracy in Turkey and its accession to Europe”, while German Foreign Minister Guido Westerwelle expressed his concern in a statement.
“We expect Prime Minister Erdogan to de-escalate the situation, in the spirit of European values, and to seek a constructive exchange and peaceful dialogue,” he said.
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