Uncertainty over the position of Cyprus' European partners to the broad thrust of the country's new proposals formed the backdrop to Friday's discussions. There are also questions over whether Russia will be involved in any final package even though a two-day meeting between the finance ministers of Russia and Cyprus broke down with no agreement.
One concrete proposal is the restructuring of Laiki, which it is estimated will generate around 2 billion euros of the 5.8 billion euros ($7.5 billion) the country needs to raise itself. If the new package is agreed by international creditors, then Cyprus will be able to secure another 10 billion euros from the eurozone and the International Monetary Fund.
A new package is necessary after Cyprus' parliament rejected a plan earlier this week to grab up to 10 percent of bank deposits.
The country needs to have the plan in place by Monday as the European Central Bank has said it will cut off emergency support to the banks. That could trigger their collapse and leave the Cypriot economy reeling. Many in the markets think that would mean the country would have to leave the euro with potentially damaging repercussions across the 17-country eurozone.
Worried Laiki employees gathered near parliament for a second day after the governor of the country's central bank announced that authorities would look to safeguard the bank's viable parts and isolate its toxic assets. The hope behind the plan is to staunch any possible contagion effects to the country's other lenders.
"The bank is finished, we'll lose our jobs and I'm worried about my kids," Laiki employee Nikos Tsiangos behind barricades and a cordon of police that have blocked the way to Parliament. "They've brought us to the brink, the Europeans wanted to destroy our economy and they've done it."
Apart from the bank's restructuring, lawmakers were looking at a number of other bills including one setting up an "Investment Solidarity Fund" and restricting banking transactions in times of crisis.
Together, they will make up at least part of the alternative plan Cyprus hopes will secure it the bailout money.
A vote on the bills was scheduled for Friday morning, but that appears to have been pushed back as lawmakers continue discussions.
Europe also appeared to turn up the pressure on Cyprus Friday. Luxembourg's finance Minister Luc Frieden told Germany's Inforadio that Cyprus "certainly must change a very great deal in its financial sector ..... I see among some euro states little financial room for more concessions to Cyprus."
Meanwhile, Cypriot efforts to clinch a contribution from Russia appear to have failed after Russia's finance minister was quoted as saying talks had broken down. Russia is a key player in Cyprus as Russian depositors have parked around 20 billion euros into the country.
Anton Siluanov, Russia's finance minister, said the Cypriots were seeking to get Russian companies to invest in a state-owned firm managing revenues from the island's newfound offshore gas deposits and give Russian companies a stake in that company.
Russian investors were not interested, he said. Cyprus also offered stakes in some of its banks, but Russian banks were not interested in that either. Siluanov also said they were not discussing the possibility of providing a new loan to Cyprus as the EU has set a debt limit for Cyprus.
However, there is still speculation that Russia may get involved in some way if the EU and the IMF sign off on the new Cypriot proposals.
Geir Moulson in Berlin and Nataliya Vasiliyeva in Moscow contributed.