Miners at Chile's Escondida voted to reject the offer from Anglo-Australian mining giant BHP Billiton but said they wanted to continue talks with the company.
Workers chanted slogans against the mine accusing the majority-owner of fiddling the numbers in its new contract proposal.
Daily production at Escondida has been cut by half since the strike started on August 7. The mine usually produces about 3,500 tonnes of copper a day.
Pedro Marin, the union spokesman, told Reuters news agency in Antofagasta on the Pacific coast of Chile: "Independent of the vote, we are going to ask the company to sit down to talk as soon as possible because we are also interested in reaching an agreement soon."
Workers rejected the company offer in a show of hands on Sunday night and on Monday afternoon the union was confirming the result in a formal ballot.
From Monday, the fifteenth day of the strike, Chilean law says that individual workers from the 2,052-member union can go back to work and make their own deals with the company, but union leaders said workers would remain loyal.
The striking miners are camped
outside the Escondida mine
Luis Troncoso, the union's president, said: "We are completely confident that none of the workers will break ranks ... and I don't think any of them is willing to break this movement.
"Our union is strong".
The strike has generated debate about fair wages in Chile as profits for copper mining firms, the backbone of the Chilean economy, have soared.
The company's latest deal included two contract options, a four-year deal and a three-year deal, and was an improvement over earlier proposals.
The four-year deal proposed the equivalent of $32,000 in bonuses and loans per worker and a 4% wage hike for the first three years of the contract with a further 1.3% raise in the fourth year.
The three-year deal included the equivalent of $23,500 in bonuses and in soft loans and the 4% rise would have been given over the life of the contract.
The union wants a bonus of $30,000 based on copper prices and a double-digit wage increase as copper prices are now five times higher than they were when the union signed its last contract in 2003.
Troncoso said: "We don't want crumbs, we're asking for 1% of the company's profits."
The company made a $2.9billion net profit in the first half of 2006.