The mayor of Concepcion city has said food is running out and police used tear gas and water cannon against looters at a supermarket on Sunday.
Rescue teams are still trying to reach dozens of people believed to be trapped in a collapsed block of flats in Concepcion.
Many Chileans in affected areas have spent the first night since the earthquake outdoors, afraid to stay inside.
Speaking to reporters on Sunday, Ms Bachelet said: "The catastrophe is enormous. The latest number I have is 708 dead."
She said 541 had died in Maule region, 64 in Biobio and a total of 103 in other areas.
More than 300 bodies were found in the devastated fishing village of Constitucion.
A growing number of people were listed as missing, the president added.
Ms Bachelet announced a series of emergency measures:
The Maule and Concepcion regions are being placed under special rules to speed up the delivery of aid
The air force will fly supplies to both areas and the military will take a leading role in distributing them
In Maule and Biobio basic goods will be handed out free of charge. Distribution points are yet to be decided.
Electricity is a big concern and the government is working to guarantee distribution
Officials said public transport services were slowly returning to normal. One metro line in Santiago is now operating. Roads are passable, although with diversions.
The airport in the capital, Santiago, has reopened, with a total of five international flight due to arrive on Sunday. It had been closed because of damage to the terminal and control tower.
Aid offered
The epicentre of the quake was 115km (70 miles) north-east of Concepcion and 325km south-west of Santiago.
CHILE QUAKE - DAY TWO
International airport reopens
Official death toll rises from 300 to more than 700
Tens of thousands forced to live outdoors because of damaged homes
Police in Concepcion move to stop looters robbing shops
Survivors rescued from collapsed Concepcion building, but dozens more unaccounted for
Limited services resume on Santiago metro and international airport
About 1.5 million homes have been damaged. Most of the collapsed buildings were of older design - including many historic structures.
About 90% of the historic centre of the town of Curico was destroyed. Many roads and bridges across the affected area were damaged or destroyed.
One US risk assessor, Eqecat, put the value of the damage at between $15bn and $30bn (£9.8bn-£19.6bn) or 10-20% of gross domestic product.
Responsibility for reconstruction will soon pass to President-elect Sebastian Pinera, who takes office in two weeks.
"It's going to be a very big task and we're going to need resources," he said.
Chile has so far not requested foreign assistance, saying it can handle the immediate relief effort.
Foreign Minister Mariano Fernandez said Chile did not want aid offers to be "a distraction", adding: "Any aid that arrives without having been determined to be needed really helps very little."
Meanwhile fears of a devastating tsunami across the Pacific receded on Sunday.
About 50 Pacific countries and territories had issued tsunami alerts.
French Polynesia and Tahiti were among those hit by high waves, but no casualties have been reported.
The Pacific Tsunami Warning Center on Sunday lifted its Pacific-wide alert.
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