Turkish protest leaders went into emergency talks with Prime Minister Recep Tayyip Erdogan on Thursday after demonstrators rejected his "last warning" to evacuate an Istanbul park at the centre of mass anti-government demos.

Thousands of defiant protesters spent another night under the stars in Gezi Park after rebuffing Erdogan's olive branch to clear out in return for a referendum on the park's planned redevelopment.

"We will stay in Gezi Park with all our demands and sleeping bags," Taksim Solidarity, the core group behind the campaign, said in a statement ahead of the meeting with Erdogan.

The fight to save the park's 600 trees prompted a brutal police crackdown two weeks ago, snowballing into nationwide protests against Erdogan and his Islamic-rooted government, seen as increasingly authoritarian.

With tensions mounting, Taksim Solidarity representatives travelled to the capital Ankara for late-night talks with Erdogan, their first since the unrest began. Local television showed around a dozen members entering the premier's residence.

Earlier, Erdogan took a combative stance against the park protesters who have put up the biggest challenge yet to the decade-long rule of his Justice and Development Party (AKP).

"I'm making my last warning: mothers, fathers please withdraw your kids from there," he said in a live television broadcast. "Gezi Park does not belong to occupying forces. It belongs to everybody."

Four people have died in the nationwide unrest so far and some 5,000 of the demonstrators, most of whom are young and middle-class, have been injured.

Erdogan on Wednesday made his first concession yet by suggesting a popular vote on plans to build a replica of Ottoman-era military barracks in Gezi Park.

The proposal came out of talks with some protest leaders, a loose coalition representing a variety of interest groups, but to the dismay of many protesters the Taksim Solidarity representatives were left out of that meeting, hardening campers' resolve to stay in the park.

"We did not suffer through the attacks... so that a referendum could take place," the Taksim Solidarity group said.

In some of the biggest clashes in the conflict yet, riot police on Tuesday stormed Taksim Square, which borders Gezi Park and had been the focal point of the protest movement.

Police fired tear gas and jets of water at tens of thousands of demonstrators, some of whom hurled back fireworks and Molotov cocktails.

Other cities across Turkey have seen similar battles.

The premier has faced condemnation from the United States and other Western allies over his handling of the crisis, which has undermined Turkey's image as a model of Islamic democracy.

The European Parliament on Thursday passed a resolution warning the government against taking "harsh measures against the peaceful protesters".

Turkish Foreign Minister Ahmet Davutoglu called the move "unacceptable", while Erdogan said he didn't "recognise any decision made by the EU Parliament".

"Who do you think you are?" he added.

NATO member Turkey has long sought to join the 27-member EU, but efforts have stalled in recent years, with concerns over the country's human rights record a key stumbling block.

As evening fell, riot police looked on as hundreds of protesters gathered peacefully around a piano in Taksim Square for a live concert, occasionally chanting: "Everywhere is Taksim, everywhere is resistance!"

Inside Gezi Park, protesters were on edge, wary about possible police intervention.

"We don't trust the government.... We will stay in the park. It's not just about the trees," said interior designer Uzay, 25, accusing Erdogan of polarising the country and curbing personal freedoms.

Istanbul governor Huseyin Avni Mutlu, who has said any police operation would only be aimed at troublemakers, took to Twitter to reassure the campers there would be no intervention without advance warning, and gave out his personal phone number to discuss their concerns.

"'The young people who are motivated by a sensitivity for the environment,' you can call me for a personal chat.... Have a good day," he wrote. His mobile phone number was retweeted 7,500 times within two hours.

While opposition to Erdogan is intense, the 59-year-old, in power since 2002, remains the country's most popular politician.

His AKP has won three elections in a row and took nearly half the vote in 2011, having presided over strong economic growth in the predominantly Muslim country of 76 million people.

Erdogan has urged loyalists to respond to the demonstrators by voting for the AKP in local polls next year.

Opponents accuse Erdogan of repressing critics -- including journalists, minority Kurds and the military -- and of pushing conservative Islamic values on the constitutionally secular nation.