Finance Minister Michael Sarris and President Nicos Anastasiades were in Brussels to discuss parameters for raising $7.5 billion, which the so-called troika -- the European Commission, the International Monetary Fund and the European Central Bank -- mandated Cyprus raise to secure a $13 billion international bailout, the BBC reported.
Cyprus has until Monday to raise $7.5 billion to secure the bailout funds.
"Significant progress has been made toward an agreement at least with the troika which will report to the Eurogroup," Sarris said. "Two or three issues need further work."
Sarris said Cyprus was considering a 25 percent tax on bank deposits of more than 100,000 euros ($130,000) in its biggest bank.
The process was thrown into disarray Tuesday when members of Parliament in Nicosia overwhelmingly rejected a tax on bank deposits. Since then, Cyprus has explored alternative funding sources, including turning to Russia for help.
Russia said Cyprus must first reach a deal with the troika, the BBC reported.
More than 1,000 Cypriot bank workers demonstrated Saturday at the Cypriot finance ministry, carrying signs that read "No to the bankruptcy of Cyprus" and chanting "United we cannot be defeated," the BBC said.
Germany has rejected a plan under discussion in which Cyprus would nationalize the pension funds of its state-run companies, a plan that included holding an emergency government bond auction. Germany also rejected the concept of ever again accepting a nation known as a tax haven into the European Union.
The tax on bank deposits in Cyprus as part of the bailout came about because of the reputation of the nation as a tax haven for criminal groups, especially for organized crime from Russia. International lenders were reluctant to provide aid for Cypriot banks because of concern it might appear they were bailing out organized crime.
Cypriot banks were heavily exposed to investments in Greece, which has helped put them in crisis.
Banks in Cyprus have been closed since Monday and are expected to remain closed until a solution to the bank crisis is found.
If there is no viable solution, Cypriot banks could fail, which could push Cyprus out of the eurozone in an exit that many believe will be severely disruptive to the eurzone's financial system.
Cyprus is also working under a deadline. The European Central Bank has said it would cut off low interest loans to Cypriot banks Monday if a solution has not been found by then. That would essentially force Cypriot banks into bankruptcy, analysts have said.
Lawmakers in Nicosia passed nine bills Friday, including one that would ban large withdrawals from the nation's banks and one that would split bank assets by creating a so-called good bank/bad bank system, which would put toxic assets into one bank that would be wound down over time.
Lawmakers also passed a bill that would allow for a tax levy on bank accounts valued at over $130,000.
That option would spare owners of smaller accounts from paying the new tax, the BBC said.