Greek Prime Minister George Papandreou will hold talks with German Chancellor Angela Merkel later to discuss his country's progress in cutting its budget deficit.
The meeting comes as policymakers decide whether to release the latest tranche of Greek bailout funds.
European leaders are trying to agree a comprehensive package to solve the eurozone debt crisis once and for all.
However, divisions remain between member states on how best to do so.
G20 leaders met over the weekend to discuss the best way forward, but EU officials stressed that no grand plan of action had been agreed.
A number of ideas were reportedly discussed, including a 50% write-down of Greece's government debts.
Other proposals included strengthening big European banks that could be hit by any defaults on national debt obligations, and boosting the size of the eurozone bailout fund.
However, late on Monday German Finance Minister Wolfgang Schaeuble cast doubt on plans to bolster the European Financial Stability Facility (EFSF).
"We are giving it the tools so it can work if necessary," he said.
"Then we will use it effectively, but we do not have the intention of boosting its volume."
On Thursday, Germany will vote on whether to approve proposals set out in July to extend the powers of the EFSF that would allow it to buy the bonds of highly-indebted countries, and to make credit available to both governments and under-capitalised banks.
'Brutal selling'
Despite Mr Schaeuble's comments, European and Asian shares rallied strongly on hopes that leaders were finally poised to act decisively.
Germany's Dax index, France's Cac 40 and the UK's FTSE 100 were all up between 2% and 3% in early trading.
Japan's Nikkei index closed up 2.8%, Hong Kong's Hang Seng rose 4.2% and South Korea's Kospi climbed 5%.
However, analysts warned the gains could be short lived.
"We've experienced these types of temporary rebounds many times before, with markets coming up for air after days of brutal selling," said Kazuhiro Takahashi at Daiwa Securities.
"Again, this will likely be a short break before we see more evidence of progress in the Greek debt crisis," he said.
Markets have been extremely volatile in recent weeks as investors worry that the debt crisis may spiral out of control. They have been critical of policymakers' inability to take decisive action thus far.
On Monday, President Barack Obama also warned of the far-reaching impact of the crisis.
"[Europe] never fully dealt with all the challenges that their banking system faced... So they're now going through a financial crisis that is scaring the world," he said.
"It's now being compounded by what's happening in Greece."
The European Commission, the European Central Bank (ECB) and the International Monetary Fund (IMF) are due in Athens this week to review Greece's progress in cutting its debt levels.
Together, they will decide on whether to release the latest tranche of bailout funds the Greek government needs to pay its bills.
