Riot police in Turkey deployed teargas and water cannon in Istanbul's central Taksim Square on Tuesday in a swoop aimed at quashing two-week-old mass street protests against the prime minister, Recep Tayyip Erdoğan.

As the police moved in on the nerve centre of the nationwide uprising, dozens of lawyers were dragged away from the city's central courthouse in what appeared to be a flagrant abuse of human rights.

On Tuesday night dozens of police were still engaged in running battles with jeering protesters in Taksim Square, firing volley after volley of teargas canisters in an attempt to drive them into side streets. Tensions remained extremely high as thousands of demonstrators streamed toward the city centre and police reinforcements were sent in.

The confrontation – which came a day after Erdoğan had promised to meet and negotiate with protest leaders on Wednesday – began just after dawn when hundreds of riot police marched toward the square armed with water cannon and armoured crowd control vehicles.

In dramatic scenes at the sprawling city's main courthouse – one of the biggest in Europe – more than 50 lawyers were dragged onto buses by riot police after staging a sit-in to support the protests centred on Gezi Park in Taksim Square.

While the police cleared the square, the park protest continued. Police briefly entered the park before withdrawing early in the afternoon.

Erdoğan sounded unapologetic and defiant in confronting the biggest challenge to his ten-year rule. "I am sorry but Gezi Park is for taking promenades, not for occupation," the prime minister said. "I invite all demonstrators, all protesters, to see the big picture and the game that is being played. Those who are sincere should withdraw. I expect this from them as their prime minister."

He attacked the international media for waging a "comprehensive" campaign aimed at sullying Turkey's image. Various unspecified international actors were determined to damage Turkey, he said.

What had started as an environmental protest aimed at saving an inner city park from being demolished to make way for an Ottoman-style shopping centre quickly snowballed into a nationwide display of anger at what is seen as Erdoğan's increasingly authoritarian stance.

Inside the park, protesters were angry and disappointed about the police operation.

"All this government does is lie," said Adnan Oruç, a 58-year-old electrician. "They speak live on television saying one thing, and I am here, witnessing the exact opposite of what they promised. That's why I am here. I cannot take their lies anymore."

Police used loudspeakers to appeal to the protesters not to throw bottles or rocks, and promised not to intervene inside Gezi Park: "Friends, we don't want to harm anyone, we don't want anyone to get hurt. Please withdraw!"

Istanbul's governor, Hüseyin Avni Mutlu, said police had no intention of breaking up peaceful protests and the aim of the operation was to remove banners hanging from the statue and the Ataturk Cultural Centre on the fringe of the square.

Several dozen riot police briefly entered the park in the early afternoon, but withdrew after facing hundreds of protesters shouting for them to leave.

"We don't trust the police or the promises of the government," said 24-year-old student Aras Özmen, organising protesters through a walkie-talkie. "But we must remain calm. We don't want any fights with the police, that's not what we are here for."

"They say that they want to clean up the square, but that's the job of the municipality, and not of the police," said Ahmet Aydin, 27. "The job of the police is to protect citizens, but instead, they attack us."

On Taksim Square, some people threw rocks and fireworks at police, who responded with teargas and water cannon. Several protesters were worried about people attacking the police, accusing those throwing rocks of needless provocation.

"They try to split our group, they try to turn us against each other, but we will not let them. This has been a peaceful movement from the start, and it will remain so," said Hamdi, 29, an architect. "We will deal with those who use violence to protest, we don't want them here. Gezi Park is no place to vent ideologies."

Some protesters could be seen trying to defuse tension several times both inside and outside the park, reminding others not to let themselves be provoked by the heavy-handed police intervention. Some wondered if some of the violent protests were staged.

"The police, the media and some provocateurs had a nice little date this morning on Taksim Square," said 31-year-old IT specialist Cumhur. "It was a very good show."

Erdoğan has repeatedly dismissed the protesters as marginal groups, "bums and looters", blaming "foreign forces" and "terrorists" for the uprisings.

In the Capulcu Teahouse inside Gezi Park, four teachers sat around a small table. None of them wanted to give their names. "Isn't it terrible that we are afraid to speak to the press freely? This is what things have come to in Turkey," said one.

According to the Turkish Medical Association, almost 5,000 people have been wounded since demonstrations broke out more than ten days ago, and three people have been killed. On Tuesday, several hundred people reportedly needed treatment in volunteer field infirmaries and hospitals, and at least one protester was said to be in critical condition.

Some wondered if the Gezi Park movement was in need of leadership to organise continued resistance. "This is a movement of civil society's dissent, and there are many groups with many demands and political views here," said Hamit Menemencioğlu, 21, manning a stand distributing food and water. "Things might be easier if we had a leader, but many people here do not want that."

In the makeshift teahouse, one teacher argued that Gezi Park was sufficiently organised: "We have everything – food, shelter, doctors, media. There is no crime here, we collect our own rubbish. We are the people, and we know what we want, we don't need anyone to lead us."

They asked for the park to remain untouched, for governors and police chiefs in cities of extreme police violence to be dismissed, for freedom of demonstration and expression everywhere, for arrested protesters to be released immediately, and for teargas to be banned.

"No matter what they say, we will stay here until these demands are fulfilled. All we are asking for are democratic rights."

The protesters appeared determined not to yield to the government's threats. "For a long time, our government has put pressure on us and we were afraid of them," said Ahmet Metin. "But now, the roles have been reversed."