Catholic priests Miguel Cabrejos and Gaston Garatea are leading the talks with senior aides of Humala after meeting with the representatives of the protesters earlier in the week.
Minas Conga is set to be Peru's biggest mining project but its future remains in doubt as opposition to its start-up grows.
Opponents say the project will damage the region's water resources but Minera Yanacocha, the company developing the mine, says it will build reservoirs to increase the water supply and will take precautions with its exploitation of the underground water resources.
Minera Yanacocha is owned 51.35 percent by Newmont Mining Corp., which has headquarters at Greenwood Village, near Denver. Compania de Minas Buenaventura S.A. has a 43.65 percent stake, while the International Finance Corp. holds the rest.
Critics say the mining project's need for vast quantities of water make it unlikely that the region's natural resource will remain unaffected by its development.
Controversy over the project has preoccupied Humala's government, which hopes to capitalize on the country's increased income from mines and minerals to fund its development program.
Peru is a major producer of gold, copper, zinc, silver and other minerals and has attracted investment deals of more than $50 billion from international companies interested in developing its mining sector.
Environmental protests and political opposition to the mineral development projects threaten to derail Humala's plans. Investment analysts said the protests could discourage investors from going ahead with their investment plans.
Minas Conga plans to have an average annual output of 580,000-680,000 ounces of gold and 155 million-235 million pounds of copper during the first five years of production, due to start in 2017. But the continuing protests threaten to put that plan in jeopardy.
A state of emergency was declared in parts of Peru earlier this month after clashes between police and anti-mining protesters caused three deaths during an attack on a government building.
Scores have been injured in protests targeting Humala's policies.
The 30-day state of emergency in Celendin, Hualgayoc and Cajamarca is expected to last through early August while security in the capital and other areas remains shaky.
Interior Minister Wilver Calle Giron called the situation "the reprehensible consequence of the violence encouraged by some leaders, who must now take responsibility."
Protests over the mining project follow riots at Lima University in which students wanting greater freedom clashed with police and tried to attack a university administration office housed in a museum.
Some student groups have also joined the anti-mining protests.
Notable deaths of 2014 [PHOTOS]