She rejected criticism of the government's handling of the disaster, which has so far officially killed at least 795 people.
"We understand your urgent suffering, but we also know that these are criminal acts that will not be tolerated," Bachelet said.
Her comments came amid growing anger that in some areas troops were standing guard over stores laden with supplies.
Meanwhile, the death toll looks set to rise sharply as relief teams reach more isolated areas.
Al Jazeera's Teresa Bo reports on efforts to recover dead and missing victims
In Concepcion, about 500km south of Santiago, the capital, residents roamed the streets looking for food and water as the first aid supplies began to arrive, four days after the earthquake.
Lucia Newman, Al Jazeera's correspondent in Concepcion, said: "There are a huge amount of soldiers deployed here ... where the worst looting has taken place since the earthquake.
"There is no power, no food and no water being distributed, but the governor here said they will begin to distribute food - in some cases house by house - later this afternoon."
An overnight curfew in the city, which was extended for a further six hours, came to an end at midday (15:00 GMT) as soldiers struggled to contain looting.
On Monday, several stores in Concepcion were set alight by mobs when troops barred them from ransacking the shelves.
More than 160 people have already been arrested as armed self-defence groups attempted to keep looters away.
Huge flames and clouds of black smoke billowed out over Concepcion as rescue teams picked through the debris trying desperately to find people still alive in the rubble.
Three more towns, Talca, Cauquenes and Constitucion, were also put under curfew - the first imposed in the country since the 1960s dictatorship of Augusto Pinochet - in a bid to restore law and order.
Teresa Bo, Al Jazeera's correspondent in Constitucion, said: "Much of the city has been devastated by the earthquake.
"Everybody we ask around here says the aid being distributed on the ground is not enough."
Patricio Rosende, the deputy interior minister, said the government had purchased all the food in Concepcion's main supermarkets so that it could be distributed for free, and more supplies were being shipped in.
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"When we have a catastrophe of this magnitude, when there is no electricity and no water, the population ... starts losing the sense of public order," Rosende said.
The measures came as Hillary Clinton, the US secretary of state, arrived on Tuesday.
Clinton came armed with 25 satellite phones to assist Chilean authorities with recovery efforts, after it dropped its initial reluctance and appealed for international aid.
"One of their biggest problems has been communications," Clinton, who will visit Brazil, Costa Rica and Guatemala after her Chile trip, said.
She was greeted by Bachelet on arrival and the two later held a news conference.
Clinton said the US would also send water purification systems and a mobile
field hospital with surgical capability that is "ready to go".
She will also meet with Sebastian Pinera, the country's president-elect.