SANTIAGO, Chile — After days of protests that have virtually paralyzed Chile, President Sebastián Piñera asked for forgiveness on Tuesday night, announcing a set of conciliatory measures in the hope of defusing the country’s worst political crisis in 30 years.

Mr. Piñera, in a televised address, acknowledged that his government and its predecessors had failed to perceive the widespread anger in Chile over economic inequality, which has fed the leaderless, spontaneous protests and violence that have spread through the country since Friday, leaving at least 15 people dead.

“I acknowledge this and I ask for forgiveness for this shortsightedness,” Mr. Piñera said.

What began last week as a student protest in Santiago, the capital, over a subway fare hike has escalated into five straight days of demonstrations in cities and towns across Chile, protesting low wages, rising prices, miserable pensions, poor health services and profound income inequality, in a country that has been touted as a regional model of economic success.