ISTANBUL — Turkey’s government offered a first concrete gesture aimed at ending nearly two weeks of street protests Wednesday, proposing a referendum on a development project in Istanbul that triggered demonstrations that have become the biggest challenge to Prime Minister Recep Tayyip Erdogan’s 10-year tenure.
Despite the offer, protesters continued to converge on Istanbul’s Taksim Squire, the epicenter of 13 days of clashes between stone-throwing youth and riot police firing tear gas, water cannons, and rubber bullets — an early sign that the proposal hadn’t defused the demonstrators’ concerns.
Word of such a referendum came after Erdogan hosted talks with a small group of activists. Many civil society groups behind the protests boycotted those talks in the capital, Ankara, saying they were not invited and that the attendees did not represent them.
The discussion was the first sign that Erdogan was looking for an exit from the showdown, and came hours after some European leaders expressed concern about strong-arm Turkish police tactics and hopes that the prime minister would soften his stance.
After the meeting, a spokesman for Erdogan’s Islamic-rooted party announced the referendum proposal at a press conference.
In a more defiant note, Justice and Development party spokesman Huseyin Celik said the ongoing sit-in in Gezi Park, next to the square, would not be allowed to continue ‘‘until doomsday.’’
But Celik also quoted Erdogan as telling the activists he met that police would be investigated and any found to have used excessive force against protesters would be punished.
The protests erupted May 31 after a violent police crackdown on a peaceful sit-in by activists objecting to a development project replacing Gezi Park with a replica Ottoman-era barracks. They then spread to dozens of cities and have attracted tens of thousands of people each night.
The proposed referendum would be over the development project, Celik said. But he said it would exclude the planned demolition of a cultural center that the protesters also oppose. Celik said the center was in an earthquake-prone area and needed to come down.
The protests took on a new flavor earlier Wednesday as thousands of black-robed lawyers stormed out of their courthouses to deride allegedly rough treatment of their colleagues detained by police a day earlier.
Sema Aksoy, the deputy head of the Ankara lawyer’s association, said the lawyers were handcuffed and pulled over the ground. She called the police action an affront to Turkey’s judicial system.
‘‘Lawyers can’t be dragged on the ground!’’ the demonstrators shouted in rhythm as they marched out of an Istanbul courthouse. Riot police stood off to the side, shields at the ready.
Erdogan has become the center of the protesters’ ire over his alleged authoritarian streak. So a referendum would be a political gamble that the government would win the vote and the demonstrators would go home.
‘‘The most concrete result of the meeting was this: we can take this issue to the people of Istanbul in a referendum. We can ask the people of Istanbul if they want it,’’ Celik said. ‘‘We will ask them: ‘Do you accept what’s going on, do you want it or not?’ ’’
In a sign of the protesters’ suspicion about Erdogan, several in Gezi Park said they thought the government would rig the referendum’s result — or balk at holding it at all.
‘‘I don’t think anything changed with that,’’ protester Hatice Yamak said of the referendum plan. ‘‘We don’t think he will do it — I think he’s lying.’’
Across Turkey, thousands of demonstrators have been mobilizing nearly every night — mostly in Istanbul in recent days. As if to let the referendum proposal sink in, the Istanbul governor, Huseyin Avni Mutlu, tweeted that riot police would not enter Gezi Park on Wednesday.
A union leader who met earlier with Erdogan suggested the government was preparing a final crackdown to quash the protests.
Bendevi Palandoken of Konfederation said that Erdogan ‘‘told me that the protests will end in 24 hours, and the police intervention will comply with European Union standards.’’
‘‘Erdogan also told me he would meet with the youngsters today and will learn their complaints,’’ Bendevi said, referring to Wednesday’s talks.
A spokesman for the prime minister could not be immediately reached for comment, and the Interior Ministry declined to comment.