Michelle Bachelet says 14,000 troops are now in the region, after dozens of people were arrested on Monday.
A BBC reporter in Concepcion says police are now posted on street corners in the city centre, but says that aid convoys are yet to reach the needy.
The death toll from the 8.8-magnitude quake now stands at 795, officials say.
Emergency workers also say 19 people are still unaccounted for.
A special air route is being set up to deliver aid from the capital, Santiago, to Concepcion, 430km (270 miles) away.
But security in the city remains a key concern after shops and homes were looted on Monday and police made large numbers of arrests.
The deteriorating security situation in Concepcion comes despite the influx of thousands of troops to reinforce local police.
"We can say that, according what we've been told from the area, the situation in Concepcion is under control today," President Michelle Bachelet said on Tuesday.
But, she added, authorities would take any "necessary measure" to stop renewed looting.
"Our principle objective is to go and help people tackle the emergency in the disaster zone.
"I want them [looters] to understand this and that they'll receive rigorous legal action. We will not tolerate such actions."
Many of the city's 500,000 inhabitants are short of food and have seen their water and electricity supplies cut off.
Aid agencies have yet to reach Concepcion, reports the BBC's Andy Gallacher, who has reached the city, and many people are still awaiting water, food and mattresses.
However, at least two police officers appear to be posted on every corner in the city centre, our correspondent says.
Some residents quoted by Reuters news agency said they were organising groups to defend their property.
Coastal destruction
Reports are also beginning to emerge of the scale of the devastation in other areas.
Up to 90% of the mud-and-wood buildings in the historic centre of Curico had been destroyed or damaged, and a hospital badly damaged, BBC reporters said.
Some coastal towns and villages were also hit by giant waves after the earthquake, with some reported to have been completely destroyed.
Reports from the town of Pelluhue suggested that a series of tsunamis swept through what was a tranquil seaside resort, destroying houses and claiming many lives.
The government admits that its attempts to provide aid swiftly have been hampered by damaged roads and power cuts.
The air supply route between Santiago and Concepcion will help the authorities send more than 300 tonnes of aid, including 120 tonnes of food, to the worst-affected area of the country.
Communication problems
International aid has begun arriving. Neighbouring Argentina is flying a field hospital over the Andes to Chile and has pledged half a million litres of much-needed drinking water.
Brazilian President Luiz Inacio Lula da Silva flew to Santiago and offered his nation's support, as did US Secretary of State Hillary Clinton.
Mrs Clinton took a consignment of satellite phones with her to Santiago after the Chilean government requested communications equipment alongside field hospitals and water purification units.
"We stand ready to help in any way that the government of Chile asks us to," said Mrs Clinton, adding: "The United States will be there to help when others leave.
After touring the disaster zone, Chilean President-elect Sebastian Pinera - who takes office on 11 March - said the situation was worse than he had expected.
"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," he said.
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 south-west of the capital Santiago.
About 1.5 million homes in Chile have been damaged. Most of the collapsed buildings were of older design - including many historic structures.
One US risk assessor, Eqecat, has put the cost of repairing the damage at between $15bn and $30bn (£9.8bn - £19.6bn) or 10-20% of the country's gross domestic product.
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