"I told them this is the moment of truth," he said.
The president said he would hold talks on Monday on a new coalition with leaders from all of the country's political parties.
Correspondents say the new administration will have a difficult task reviving the economy of the country of 2.4 million people.
Latvia's economy has shrunk at its fastest rate since the early 1990s, after it split from the Soviet Union and regained its independence.
Latvia's gross domestic product (GDP) fell 10.5% in the last quarter of 2008, compared with the same period a year earlier. Economists believe GDP could fall as much as 10% this year.
The country had enjoyed several boom years - in 2006 the economy was still growing by 12% a year - but the global credit crunch has hit Latvia hard.
Correspondents say a major reason for the decline was that locally-owned banks, which make up 40% of the Latvian financial system, were taking deposits from abroad and investing them in the booming property market.
When the property market begin to decline and foreign credit dried up, confidence in Latvian banks evaporated.
The second largest bank, Parex, collapsed after depositors panicked and has been largely nationalised.
In December 2008 the Latvian government was forced to seek 7.5bn euros (£6.6bn; $9.5bn) from the IMF, World Bank and EU to bail itself out. As part of the deal it has had to cut public spending and increase taxes - both unpopular policies.
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