Southern Copper Corp. President Oscar Gonzalez said in a statement Friday that the "pause" would let all sides air concerns and "identify solutions."
Protesters in Cocachacra, the epicenter of the conflict, say they have no intention of backing down from their demand that the $1.4 billion Tia Maria project be cancelled.
Locals fear it will contaminate crops in the fertile Tambo valley. The company says the project would will take water from the Pacific Ocean and return it there after processing.
Earlier Friday, President Ollanta Humala said cancelling the project would expose Peru to lawsuits and make it less attractive to investors.
Protests against the project in 2011 also claimed three lives.