"We had a very good first meeting -- a very constructive, very honest discussion. We underscored how difficult the situation is and we will now continue our discussions to find a solution by which we hope we will be getting some support from Russia," the finance minister said after meeting for 90 minutes with Russian Finance Minister Anton Siluanov.
Sarris called the meeting "a good beginning," and said talks would continue.
The meetings are taking place a day after members of Parliament in Cyprus rejected a $13 billion bailout proposal from the European Commission, the International Monetary Fund and the European Central bank, known as the troika.
That plan stipulates that Cyprus come up with $7.5 billion itself. The plan lawmakers rejected Tuesday called for a tax to be levied on bank deposits, a strategy that is, in part, due to concerns that deposits in Cypriot banks include huge amounts of ill-gotten gains from Russian criminals.
That plan was not only rejected soundly by lawmakers, but was harshly criticized by Russian President Vladimir Putin, The New York Times reported Wednesday.
Russia has already loaned Cyprus $3.2 billion. Part of the talks between the finance ministers included an extension of that loan and a possible reduction in the loan's 4.5 percent interest rate.
Britain's The Guardian newspaper said Cypriot President Nicos Anastasiades met with Orthodox Archbishop Chrysostomos II, who has offered to put the church's property in Cyprus up for collateral.
A government spokesman said the president was looking for a solution that would "reduce the $7.5 billion haircut from depositors, by borrowing from our own resources."
One observer said Cyprus did not understand international expectations.
"The Cypriot members of Parliament obviously didn't get the EU [European Union] memo that states that you must vote yes, and if you don't, you keep voting until you do," said market analyst Michael Hewson at CMC Markets.