actors and artists but also including two members of the umbrella protest group Taksim Solidarity, hours after saying his patience had run out and warning protesters occupying Gezi Park to leave.
Separately, Istanbul Governor Huseyin Avni Mutlu offered to meet demonstrators from Taksim Square, the epicentre of the protests, at a cafe by the Bosphorus waterway to discuss their demands that the government abandon plans to build a replica Ottoman-era barracks on the park, which adjoins Taksim.
"For those who want to talk face to face tonight, from midnight we will talk in groups, if necessary until morning," Mutlu said on his Twitter account.
A police crackdown on the park nearly two weeks ago triggered an unprecedented wave of protest against Erdogan and his AK Party - an association of centrists and conservative religious elements - drawing in secularists, nationalists, professionals, unionists and students.
Erdogan has already discussed the plans to build over the park with various people who support the protesters, but had refused until Thursday to meet with the Taksim Solidarity group at the heart of the campaign to protect it.
Late on Thursday, he appeared to suggest that hundreds of protesters, camped out in a ramshackle settlement of tents in Gezi Park, could be forcibly evicted, although Mutlu said later there were no such immediate plans.
"Our patience is at an end. I am making my warning for the last time. I say to the mothers and fathers, please take your children in hand and bring them out ... Gezi Park does not belong to occupying forces but to the people," Erdogan said.
Taksim, where police fired teargas and sent thousands scurrying into side streets two nights ago, was crowded but calm overnight. Some of the assembled masses chanted and danced, while others listened to a concert pianist who has taken up residence amid the protesters.
Riot police guarded a statue of Mustafa Kemal Ataturk, founder of the modern Turkish republic, on one side of the square and the Ataturk Cultural Centre on the other, both of them targets for protesters to hang flags in recent days.
Police fired teargas and water cannon day after day in cities including Ankara last week, while youths threw stones and petrol bombs in Turkey's worst unrest for years.
Three people, including a policeman, died and about 5,000 people were injured, according to the Turkish Medical Association.
Erdogan met an earlier group of academics, artists and students who support the Gezi Park protests on Wednesday and AK Party Deputy Chairman Huseyin Celik said they discussed the possibility of a referendum on the plans to build on the park.
The offer is one of the only concessions the authorities have publicly floated after days of firm rhetoric from Erdogan refusing to back down. Celik gave few details of how a referendum would be carried out, saying it could either be held across Istanbul, or just in the district near Taksim.
The protesters in Gezi Park were sceptical following that first meeting, saying the delegation was unrepresentative and rejecting the idea of a referendum, saying their demands -primarily that the construction plans be halted - were already clear and did not require a vote.
It was not clear whether Thursday night's talks would be met with the same scepticism.
Erdogan's tough political style has endeared him to voters -who have handed him an increasing share of the vote over the past three elections - but his opponents say he has poured fuel on the flames with his robust response to the protests.
The United States has voiced concern about reports of excessive use of police force, while the European Parliament on Thursday warned the government against the use of "harsh measures" against peaceful protestors and urged Erdogan to take a "unifying and conciliatory" stance.
The comments were not welcomed by Ankara. "Turkey is not a nation that needs to be taught a lesson in any way on these topics by any country or by any group of countries," Foreign Minister Ahmet Davutoglu said.
Erdogan, who has accused foreign forces, international media and market speculators of stoking unrest and trying to undermine the economy, said he would "share with the nation" on Friday details of what he called a "game being played with Turkey."
"It is as if the whole of Turkey is on fire, as if the whole of Turkey is collapsing," he said of some media coverage, describing it as "deceptive and unethical."