The start of the Eurogroup talks were postponed by two hours, to 8 pm (1900 GMT), amid high-level talks between Cypriot President Nicos Anastasiades and top officials from the European Union, eurozone, ECB and International Monetary Fund (IMF), DPA reported.
Sunday's talks come after a deal reached by Cyprus and its international partners was rejected by parliament in Nicosia last week, after a levy on small depositors fuelled outrage.
Cyprus had been loathe to apply a levy on depositors, but Nicosia is now proposing a levy on deposits of more than 100,000 euros (130,000 dollars). Smaller deposits would reportedly be spared.
However Austrian Finance Minister Maria Fekter warned that "right now, nothing can be ruled out." She insisted however that pensioners not be hit by the bailout measures.
"I hope that we can reach an outcome tonight," said German Finance Minister Wolfgang Schaeuble, adding: "of course that is on condition that the situation is seen fairly realistically in Cyprus."
"The parameters for a solution exist, but the devil is in the detail," said French Foreign Minister Pierre Moscovici.
Spanish Economy Minister Luis de Guindos said it was "fundamental to have a credible solution," while Moscovici said Cyprus had to contribute its share to fix the country's "casino economy."
"We need a solution tonight," said Luxembourg Finance Minister Luc Frieden, "We need to create stability and I believe we need to think very carefully about what this stability is worth to us," he added.
He and other ministers ruled out a Cypriot exit from the eurozone.
Frieden said there had been no talk of increasing the share demanded of Cyprus to make up the difference between its estimated need of 17 billion euros and the 10 billion euros that international creditors are prepared to provide.
But Schaeuble warned that Cyprus's needs had "possibly worsened" during the last week.
"My own view is the position has deteriorated in the week, because uncertainty always causes greater difficulties," Noonan said.
Ministers played down fears of contagion, stressing that Cyprus was a unique case, due in part to the disproportionate size of its banking sector.
En route to Brussels, Anastasiades reportedly stopped off in Athens to stop the sale of the Greek branches of Cypriot lenders - a move that would have piled more than 5 billion euros of bad assets onto the Bank of Cyprus.
Cypriot authorities have spent the weekend trying to hash out a deal in Nicosia with its international creditors, after Nicosia's parliament passed measures restricting the movement of capital out of the country and approving the establishment of a solidarity fund.
The Europeans and the IMF were asking for a bank deposit tax of 18 to 22 per cent for the country's largest lender, the Bank of Cyprus, Kathimerini newspaper reported, adding that all other banks could face a levy of 4 per cent.
Other elements under consideration include splitting the country's second-largest lender, Laiki Bank, into a "good bank" - holding all deposits up to 100,000 euros - and a "bad bank" comprising larger assets, which may never be recovered in full.
Big depositors that could be hit by the measures include many of Cyprus's major companies and foreign investors, notably from Russia.
Negotiations reportedly stalled over IMF demands that the Bank of Cyprus take on Laiki's healthy assets but also around 9.5 billion euros of debt - a step that Nicosia fears will ruin the country's largest bank.
Discussions late Saturday were "explosive," sources said.
Meanwhile on Sunday, the Cypriot Central Bank imposed a daily 120-euro withdrawal limit at ATM machines for all local banks, according to broadcaster RIK.
The country's banks, which have been closed since March 15 to avoid a bank run, are due to reopen on Tuesday.