The government of President Ollanta Humala badly wants the project to go ahead and as part of its fight-back has suggested the protesters are mostly local agrarian residents and peasants who don't understand scientific explanations the mine poses no risks to underground water sources, lakes and rivers.
Officials accused the protesters' representatives of intransigence and unreasonable behavior.
The protesters, far from being content with a suspension in the operations, want the project canceled as they say the risks for the water resources will remain so long as the project remains alive.
The $4.8 billion gold and copper mining project is planned to be Peru's biggest but as protests turn increasingly violent its fate remains unclear.
Humala in previous pronouncements announced the safety of water resources would take precedence over exploitation of the gold and copper deposits. Protesters' representatives aren't reassured.
As clashes between law enforcement officers and protesters continue, casualties have been reported and material damage is mounting. Clashes earlier in the week left at least 20 people injured, some with gunshot wounds.
The Conga mine is to be operated by Colorado company Newmont Mining, which also runs the Yanacocha open-pit gold mine 20 miles to the north.
Newmont is the majority owner in Conga, which is to begin production in 2015 and is an outgrowth of Yanacocha, Latin America's biggest gold mine. The Yanacocha consortium includes the Peruvian company Buenaventura Mining Co. and the International Finance Corp.
However, leaders of the protest said the planned mine project could devastate the region's ecology and nothing short of its cancellation would persuade them to end the protests. They said they would insist on a legal document confirming the cancellation.
Analysts said such a cancellation would be unprecedented and would open the way for claims against another 60 potential water contamination points that environmentalists have pinpointed so far.
Cajamarca is one of the most heavily mined states in Peru. The country earns more than 60 percent of its total export income from mined products.
Buenaventura said it considered suspension "a prudent decision in order to re-establish law and order in the Cajamarca Region that is under social unrest."
It said it still considered Conga a feasible mineral deposit and believed the well-being of the people in Cajamarca moving forward depended on the development of this and other mineral deposits in the region.
Buenaventura Chief Executive Officer Roque Benavides said, "Suspending construction activities in Conga does not mean that we do not believe in the project.
"We think this is the best thing we can do for the people in Cajamarca and for the country," he said.