Lithuania gets more than 80% of its gas and most of its oil from Russia.
The country is also under pressure from the EU to close its Ignalina nuclear power station this year. The closure was a condition for Lithuania's EU accession in 2004.
Ms Grybauskaite's powers to steer the economy are limited, however, as the presidency is more focused on foreign policy.
But she pointed to her power to issue decrees, "which are obligatory to the government".
The size of her victory also gave her authority and "moral power" in Lithuania, she said.
Like its Baltic neighbours, Lithuania has been hit hard by the global economic downturn. Its economy is expected to contract by as much as 15% this year and in January frustration over the crisis escalated into rioting.
"I hope to be a stabiliser in this situation," said the president-elect, who will have the right to veto the budget if she so chooses.
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