Angered by a mounting death toll since unrest erupted last month, calling for sweeping change and blasting the government and police for deadly clashes in the southern cities of Ayacucho and Juliaca.
They want President Dina Boluarte to resign, then snap elections and a new constitution.
"Dina, assassin, the people reject you," they chanted.
But on Thursday night Boluarte accused protesters of vandalism and vowed they'd be subject to the "full rigor of the law."
"That was not a peaceful protest. The violent acts that occurred in December and January will not go unpunished."
This building in the city's historic center caught fire.
Police estimated the march at around 3,500 people, but others speculated it attracted more than double that.
The mounting death toll in the worst unrest Peru has seen in two decades stands at 45, with the latest victim on Thursday, according to government figures.
Over the past month, many from Peru's poorer, rural regions have vented anger at the Lima establishment over inequality and rising prices.
The protests were sparked by the dramatic ouster of leftist former President Pedro Castillo in early December after he tried to illegally close Congress and consolidate his grip on power.
