European officials were cautious about the prospects of reaching a comprehensive deal on Monday to keep Greece from defaulting and falling out of the currency union, despite optimism in financial markets, CTV News reported.
Greece needs more loans from its creditors, which include its fellow eurozone states and the International Monetary Fund, in time for June 30, when it faces a debt repayment it cannot afford. The country has been negotiating for four months what economic reforms it should make to get the money.
After Monday's meetings of eurozone finance ministers and European leaders, another leaders' summit is planned for Thursday and Friday.
Jeroen Dijsselbloem, who heads the eurozone meetings of finance ministers, said it would be impossible to get "a final assessment" on Monday.
Ahead of the meetings, Greek Prime Minister Alexis Tsipras made new proposals on the economic reforms and budget cuts his country would accept. European Commission President Jean-Claude Juncker said they were a sign of progress but warned that "we are not yet there."
No details of the proposals were made public, but investors were hopeful that they represented a long-awaited compromise.
The Athens stock index was up 6.4 per cent while Stoxx 50 of top European shares was 2.9 per cent higher.
Despite the market rally, tension was palpable in Greece, where people flocked to cash machines to withdraw money. The concern is that a debt default by Greece could destabilize the country enough that it might have to eventually leave the euro.
To support Greek banks in the face of growing money withdrawals, the European Central Bank increased the amount of emergency credit it allows the banks to draw on, a banking official said.
The official, who spoke only on condition of anonymity because the decision had not been made public, said the ECB remains on call in the coming hours and days to revise the amount of credit to Greek banks.
Reports indicate Greeks withdrew about 4 billion euros last week.
Yannis Nikolopoulos said that a deal between Greece and its creditors "is mandatory at all costs, otherwise we're doomed."
An exit from the euro would be hugely painful for Greeks, plunging the country back into a deep and long recession.
Greece has a debt repayment on June 30 worth 1.6 billion euros that it cannot afford without more loans. The talks are currently about releasing the last 7.2 billion euros in the country's bailout program, which expires at the end of the month.
Since coming to power in January, the new government has refused to make more budget austerity measures, which it blames for devastating the economy. It has since softened its approach, but it remains reluctant to take the steps creditors demand.
Before leaders gather on Monday evening, eurozone finance ministers will also gather in Brussels to pore over the details of Greece's proposal and confirm whether it meets the demands of creditors.