Greece has committed to work intensively with international creditors to resolve outstanding issues holding up its access to bailout loans, according to German Chancellor Angela Merkel.
The creditors have made clear that Greece must improve an offer of reforms it would introduce in exchange for €7.2 billion in bailout loans it needs to repay debts due at the end of the month.
Mrs Merkel said that in overnight talks with Greek Prime Minister Alexis Tsipras a clear consensus emerged that "Greece will now work emphatically and at full steam with the three institutions in coming days to try to clear up all the outstanding issues".
She expressed "hope that the necessary progress can now be made" and underlined that "each day counts".
In early trading, the Athens stock exchange was up 5.5 per cent on hopes of an impending deal. European markets were up too, with the Euro Stoxx 50 index gaining 0.7 per cent.
Mr Tsipras plans to meet with Jean-Claude Juncker, the head of the European Union's executive Commission, which is helping to supervise Greece's bailout programme.
After his talks overnight with Mrs Merkel, Mr Juncker and French President Francois Hollande, the Greek premier said: "We decided to intensify the effort to bridge the remaining differences."
The lack of progress in the negotiations over the past weeks has revived fears Greece could default on its debts and drop out of the euro, a move that would create huge uncertainty for Europe and global markets.
Piling new pressure on Athens, Standard & Poor's in New York downgraded Greece's credit rating one notch on Wednesday, saying it's likely the country will default on its commercial debt within a year if it can't strike a deal.
Another ratings agency, Moody's, noted that while Greece's problems were mounting, there appeared to be little impact on the markets of other eurozone states, even the economically weaker ones.
Finance ministers from the 19 nations using the euro currency will meet in Luxembourg next Thursday, less than two weeks before Greece's bailout programme expires and it has a big debt repayment due.