Garcia replaced his cabinet earlier this month following allegations of corruption in a bid to raise his approval rating, which has been around 20 per cent.
Yehude Simon, a prominent leftist, was named prime minister in a move partly aimed at countering concerns that social programmes for the poor would not be a priority for his government.
Around 40 per cent of Peruvians live in poverty and have seen little relief despite seven years of economic growth.
Critics say Garcia has not done enough during two years in office to fairly distribute wealth from mining exports.
Simon, who was jailed for eight years in the 1990's over ties to the armed communist group Tupac Amaru, has said he would not tolerate violent demonstrations, and would only negotiate once public roads were unblocked.
"If they want to talk, they can come talk. We aren't closing any democratic space," he said.
He told protesters in Moquegua that they would have to cede control of a captured bridge before congress would vote on a bill to devote more mining royalties to local authorities.
Antero Flores, Peru's defence minister, also said the government would not be forced into making concessions.
"I think discipline must be imposed. Dialogue is important but not when a gun is aimed at your head," he said.