MPs in Cyprus are due to begin voting on a series of bills that aim to raise the funds the country needs to secure an international bailout.
The country is in a race against time after the European Central Bank gave Cyprus until Monday to find the money.
If it does not, liquidity to the country's banks could be cut off and they could collapse.
Cypriot President Nicos Anastasiades has been holding talks on the crisis with the EU-IMF "troika".
Meanwhile, talks on new Russian financial aid for Cyprus have failed, Russia's finance minister confirmed.
Anton Siluanov, speaking after talks with his Cypriot counterpart Michael Sarris, said Russian investors were not interested in Cyprus' offshore gas reserves.
Mr Sarris, who has now left Moscow, had reportedly been seeking some 5bn euros (£4.3bn; $6.5bn) in return for bonds in energy and other assets, according to a report by Bloomberg news agency.
Cyprus needs to find 5.8bn euros to qualify for a 10bn-euro bailout loan from the troika, which is made up of the European Commission, the European Central Bank (ECB) and the International Monetary Fund. Parliamentarians flatly rejected a plan to tax bank deposits earlier this week.
European Commission chief Jose Manuel Barroso, who is also in Moscow this week, said he was "very concerned" at recent developments in Cyprus but added: "We have in the past solved bigger problems."
"I hope that this time a solution can also be found."
MPs could be seen arriving at parliament in the capital, Nicosia, passing protesters.
Eurozone finance ministers have said they are "ready to discuss with the Cypriot authorities a draft new proposal", which they expect "the Cyprus authorities to present as rapidly as possible".
Political leaders discussed the options with President Nicos Anastasiades on Thursday, and the package was then discussed by the cabinet. But MPs said they needed more time to study the nine bills that make up the draft legislation.
If no "Plan B" can be found by Monday, the ECB may cut off funding to the island's banks, it said in a statement, triggering their collapse and possibly the country's exit from the euro.
Anxiety is growing as the country - and the eurozone - enter a critical few days, says the BBC's Mark Lowen in Nicosia.
Both Bank of Cyprus and another big bank, Laiki, are believed to be reliant on the ECB's Emergency Liquidity Assistance, provided via the Central Bank of Cyprus.
All Cypriot banks have been shut until next Tuesday to prevent mass withdrawals.
A key component of "Plan B" is the establishment of a state "investment solidarity fund" which would issue bonds on state assets to raise the 5.8bn euros required.
Other elements could include restructuring other Cypriot banks, use of pension fund, and accepting an offer of help from Cyprus' wealthy Orthodox Church.
A revised levy on deposits also remains a possibility.
Big Russian investors are believed to hold about a third of all Cypriot deposits - and reacted with fury when the initial plan to tax deposits by up to 9.9%.
Russia gave Cyprus an emergency loan of 2.5bn euros in 2011. Mr Siluanov said that no new Russian loan had been on the table with Mr Sarris because of limits imposed by the EU on Cypriot borrowing.
Mr Sarris had proposed instead setting up a Cypriot state company offering bonds to Russian commercial investors, the Russian finance minister said.
"Our investors examined this issue and showed no interest," he added.
Earlier, Russian Prime Minister Dmitry Medvedev attacked the original bailout proposal for a levy as "absolutely absurd".
"I think that the Eurogroup [the group of eurozone finance ministers] ought to look at further plans for a settlement around Cyprus with the involvement of all interested parties, including Russian structures," he said, speaking after talks with Mr Barroso in Moscow.
Any revenue from gas discoveries off Cyprus remains years off and Turkey may challenge its exploitation.
The banking sector dominates the economy and if a viable rescue is not organised soon the island state risks having to abandon the euro.
Cypriot banks were among the bondholders who had to take a big "haircut" in the second massive bailout for Greece.
Eurogroup chairman Jeroen Dijsselbloem told the European Parliament he doubted a "Plan B" was really possible - and he partially defended the original idea of a levy on deposits, saying "alternatives would have made Cyprus' debt unsustainable".
Since 2008 the eurozone has been badly bruised by the massive bailouts provided for Greece, the Republic of Ireland and Portugal. There is a widespread reluctance to commit more EU taxpayers' money to ailing banks in southern Europe.