"Chile has the resources for a number of actions, but we will have to ask for credit from the World Bank and other entities," Ms Bachelet said.
President-elect Pinera is set to take office next week.
He said his government would be one of reconstruction, with a plan of four clear stages - "to cope with the emergency needs of citizens, find people who are still missing, provide prompt and timely assistance to the sick and wounded, and restore law and order so that people can return to peace".
UN Secretary General Ban Ki-moon is to visit Chile on Friday to assess the damage and meet Ms Bachelet and Mr Pinera.
An 18-hour nightly curfew remains in place in Concepcion, Chile's second largest city, and six other towns badly affected by the earthquake.
Officials have said 802 people are confirmed to have died, of whom 279 have been identified. But there are reports of many people still missing in the coastal town of Constitucion.
About two million Chileans are believed to have been affected by Saturday's 8.8 magnitude earthquake, the seventh most powerful on record and the worst disaster to befall Chile in 50 years.
The epicentre of the quake was 115km 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.
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