Pedro Marin, the union secretary, said: "We are optimistic. The workers are calm ... plus there's going to be a labour mediator present.
"There are six points left to be negotiated, including the toughest issues, salaries and bonuses."
The Chilean company stopped operations at the mine on Friday after workers had illegally blocked access roads to the mine for two days. The company said the blockages had put the health and security of the people working there at risk
Global copper prices have soared as a result of the strike. The benchmark three-month copper contract on the London metal exchange jumped as much as $265 to $7,555 a tonne, before last trading at $7,420.
The mine, which produces 8 percent of the world's copper, is owned by leading global miner BHP Billiton.
Up until the halt of mining operations, Escondida said it was producing more than half of its normal output, which is roughly 3,500 tonnes of copper a day, and losing some $16million in net profit a day.
Escondida said: "The company wants to maintain its operational continuity and renew operations as soon as possible, as soon as the police can ensure the full safety of people who work in the company."
Luis Troncoso, the Union president, said that the company was trying to weaken the union at a critical time.
Referring to Chilean labour law, which allows individual workers to go back to work if a union strike goes on for more than two weeks and to make their own deals with the company, Tronsco said: "After the fifteenth day [of a strike] the company can negotiate individually with the workers.
"They know they don't have any more production in the mine at this moment, so the only way out for them right now is to halt operations."
Escondida's 2,052-member union walked out on August 7 demanding a substantial raise and a special $30,000 per worker bonus linked to record high copper prices.
Escondida's net profit soared to $2.9billion in the first half of the year due to a prolonged copper price rally fuelled by tight supplies, booming Chinese demand and new investor interest in commodities.
Escondida, also part owned by Rio Tinto Ltd., produces about 1.3million tonnes of copper per year, more than 20 percent of annual output in Chile, the world's largest copper-producing country.