Mrs Bachelet has warned that looting and crime is "not acceptable".
"I want to call to the people's conscience. We must all work together," she said.
The army was called in to help the police force deal with looters, some of whom filled shopping trolleys with groceries while others made off with plasma TVs and other electrical appliances.
Some 160 people were arrested for looting and breaking the curfew, police said on Monday.
During the clashes, one 22-year-old man was shot and killed.
And by Monday evening tensions had flared once more, with troops deployed to the streets after a blaze began in a looted supermarket.
Chilean newspaper La Tercera reported that despite the presence of troops, a huge fire was intentionally started at a building housing the Polar department store.
The blaze caused the building to collapse, La Tercera reported. Marco Riquelme, a regional spokesman for the department store, told La Tercera the incident was a "clear example" of the "chaotic situation" survivors were enduring in Concepcion.
Chile firefighters tackle blaze
Hospital set to collapse
Reports are beginning to emerge of the scale of the devastation in areas south of the Chilean capital, Santiago.
AT THE SCENE
BBC News, Curico
In the main square in Curico, the authorities have set up an emergency radio station. Most of Curico's residents are on the streets trying to secure government help to investigate the extent of damage to the small town, which lies about 200 miles from the epicentre.
The vast majority of its old town has been destroyed and as much as 90% of the mud and wooden buildings in the historic centre have either crumbled or have to be demolished.
The town's mayor said that one of the main problems was the hospital. The pillars have collapsed, he said, and the structure won't stay up much longer.
Meanwhile the coastal region near here has been even more badly affected. It's understood that entire villages have been destroyed either by the earthquake or by a subsequent tsunami.
A BBC team that reached the town of Curico, between Santiago and Concepcion, said 90% of the town historic centre had been damaged.
The town's Mayor, Hugo Rey Martinez, told the BBC's Will Grant the hospital building was compromised and would soon collapse.
However, food and water was being distributed and the situation was comparatively calm, our reporters said.
In coastal towns and villages hit by giant waves after the earthquake, the scale of destruction is becoming clear.
More than 300 bodies were reportedly found in the fishing village of Constitucion alone. The mayor of Constitucion said the town's seafront and centre had been "completely destroyed".
In the port of Talcahuano, more than 20 boats were swept ashore and dumped in the streets by the waves.
Relief efforts are beginning to get under way, with the United Nations pledging to send aid quickly to the earthquake zone.
Many of Concepcion's 500,000 inhabitants are short of food and have seen their water and electricity supplies cut off.
UN officials say the president has asked for mobile bridges, field hospitals, satellite phones, electrical generators, water purification systems and field kitchens, as well as experts able to assess the relief needs.
The international community has been pledging aid to Chile.
Australia - placed on tsunami alert after the huge quake - promised $4.5m in emergency and reconstruction aid. The European Commission has already approved three million euros ($4m) in emergency funds, Japan has promised $3m and China $1m.
Neighbouring Argentina is sending some 50 health professionals as well as water treatment systems.
About two million Chileans are believed to have been affected by Saturday's earthquake, the seventh most powerful on record and the worst disaster to befall Chile in 50 years.
The epicentre of the quake was 115km (70 miles) north-east of Concepcion and 325km (200 miles) south-west of the capital Santiago.
With each aftershock - and there were more than 90 over the next few hours - we felt everything was going to start again
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