“We are at war against a powerful enemy, who is willing to use violence without any limits,” he said in a televised address from the Chilean Army’s headquarters in Santiago.

He blamed organized criminal groups for the violence.

The president’s remarks were widely viewed as incendiary, and on Monday, Gen. Javier Iturriaga , the national defense chief, who is also in charge of security around the Santiago metropolitan area, distanced himself from them.

“I’m not at war with anybody,’’ General Iturriaga said.

Mr. Piñera himself took to the airwaves Monday evening, telling his fellow citizens in a speech that he had been speaking with leaders of congress, mayors and others.

On Tuesday, he said, he will meet with political leaders, including members of the opposition, “to explore and advance toward a social agreement that may bring us closer to better solutions to the problems faced by Chileans.”

“This is the first step of a long road,” Mr. Piñera said.

The demonstrations started over a subway fare increase two weeks ago, which Mr. Piñera canceled on Saturday night. But his move failed to quell the wave of demonstrations, and on Monday protesters returned to the streets in defiance of the military.

“Everything has to burn,” said Alexis Toro, a 24-year-old student on his way to a demonstration on Monday. “The president announced he would wage war on the people, so he is getting his war.”