Huascar said farmers would continue their protests until the government agrees to negotiate. Police were able to reopen portions of some routes late on Monday, but travellers complained of protesters throwing rocks.
At least one person died, the government said.
Jorge del Castillo, the head of the cabinet, told reporters: "The government demands the protest be ended and roads be opened without having to resort to military force.
"The army and the police will act immediately if necessary."
Peru signed the free-trade agreement in December and plans to forge deals with China, Canada and Mexico soon.
The country's farmers, already angered by the rising cost of fertiliser, want debt relief and say the US trade deal will flood local markets with imports of subsidised US agricultural goods.
But the Peruvian government says the trade pact will give farmers access to the US market.
Alan Garcia, the Peruvian president, is pushing free trade as a way to lift incomes in a country where about 12 million people live in poverty despite living in one of the world's fastest growing economies.