Celik said the government could hold a referendum on the redevelopment of the park, the last green space in central Istanbul -- but he urged the demonstrators to "walk out."
At least one protester immediately rejected the idea of a vote.
"We do not think that a referendum is the right way to go because we think that this park should remain as a park because it`s our right, and rights should not be asked in a referendum," said Imre Azem.
The meetings took place a day after riot police used massive amounts of tear gas, water cannons and stun guns to break up protests in Istanbul`s Taksim Square. Police also shot tear gas canisters into nearby Gezi Park, violating a promise not to do so.
Leaders of the protests skipped Wednesday`s talks. One of them, Eyup Muhcu, said those attending the meeting are friendly with Erdogan`s government. Meanwhile, thousands of lawyers marched out of their offices in several cities to rally against the arrests of attorneys in the protests.
With no sign of negotiations on the horizon, Turkey, a NATO ally with a democratically elected government, could see fighting grip more of the country. And harsh actions against protesters could strain Erdogan`s strategic friendships with much of the West -- relationships that are particularly critical in light of the civil war ravaging Turkey`s neighbor, Syria.
"The real challenge for the government of Turkey, as now the international focus is on this crisis: How do they get the people behind me to agree to go home?" CNN`s Nick Paton Walsh reported Wednesday from outside Gezi Park, seat of the demonstrations. "That requires compromise, conciliation."
On Wednesday morning, Paton Walsh saw someone being taken out of the park on a stretcher. But things were calm in the area, with morning rain having washed away some of the debris from events the night before.
Traffic in the major square was nearly back to normal. While police were in position, they looked relaxed, CNN`s Arwa Damon reported. Police worked to dismantle barricades that demonstrators in the square have used as they`ve battled police in recent days.
In Ankara, street skirmishes broke out between protesters and police, who fired tear gas.
More about: