Chilean President Michelle Bachelet said that two million people had been affected by the earthquake.
The 8.8 quake is one of the biggest ever recorded and the largest to hit Chile in 50 years.
National television quoted unnamed disaster officials as saying 350 deaths in the coastal town of Constitucion, close to the epicentre, had been caused both by the quake and the tsunami it set off.
Many Chileans in affected areas have spent the first night since the earthquake outdoors, afraid to stay inside.
Chilean TV showed pictures of a devastated stretch of coast south of Valparaiso, with upturned boats, wrecked homes, and people forced to sleep outside.
In Concepcion, close to the epicentre, officials said 25 people had been rescued from a collapsed building but dozens who were believed to have been trapped inside were still unaccounted for.
There are long queues at many shops and petrol stations.
TV pictures also showed people removing goods from a supermarket in Concepcion, Chile's second city, despite efforts by police to clear the crowd with tear gas and water cannon.
AT THE SCENE
Gideon Long, BBC News, Santiago
The streets of the capital, usually buzzing with activity on a summer weekend like this, are eerily quiet and dark. Nearly 24 hours after the quake struck, whole swathes of the city have no electricity and no running water.
Many people have packed up and left to stay with friends and relatives who are better off than they are.
The city's new buildings seemed to have survived more or less intact. But it's the old buildings that suffered. I drove past my local church - still intact but missing its dome, which crashed to the ground when the earth began to shake.
Around the city of Concepcion, whole villages have been flattened. Highways have been sliced in two and bridges have collapsed.
But help is arriving. Chile has a long history of earthquakes and the authorities here know how to deal with them.
The epicentre of the quake was 115km (70 miles) north-east of Concepcion and 325km south-west of Santiago.
Chilean officials and ministers are still trying to come to terms with the scale of the disaster.
Interior Minister Edmundo Perez Yoma said it was difficult to give precise figures of a "catastrophe of immense proportions".
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.
About 1.5 million homes have been damaged and police patrols have been stepped up to deter looters.
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.
Officials said public transport services were slowly returning to normal. One metro line in Santiago is now operating. Roads are passable, although with diversions.
Efforts are under way to get aid to victims, with relief supplies being sent to the Juan Fernandez islands, where at least five people were killed as tsunamis hit.
The coastal town of Talcahuano, badly damaged by tsunami waves, is said to be the worst affected.
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 QUAKE - DAY TWO
International airport reopens
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
Officials say Santiago metro will soon be working and other transport returning to normal
Pacific-wide tsunami alert lifted after fears most of the region is spared high waves
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.